Need help to derive “X” from this complex equation

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Titanus

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Hi, I’m new to this forum seeking your help to find the way to get final equation to derive “X” value.
I’ve tried my best to simplify my initial equation to the one posted below.
I’m struggling to pull out my X from function (X - Y) / (X + Y).
Any suggestion for next step to get my X ?
B271EBA0-7A73-48BB-8C06-88A0D13A42D3.jpeg
 
I’m struggling to pull out my X from function (X - Y) / (X + Y).
Click to expand...
What do you mean by that? Are you trying to express Y as a function of X when (X-Y)/(X+Y)=C for some constant C?
As for solving that long hairy equation I would start with replacing some of sub-expressions (like [imath](V+((L_2-1)\times p)[/imath] and all left hand side) by some new names, then reducing the fractions in the right hand side to a common denominator, etc.

As always, it would be easier to help you if you showed us what you have already tried and where do you feel you are stuck.
 
blamocur said:
What do you mean by that? Are you trying to express Y as a function of X when (X-Y)/(X+Y)=C for some constant C?
As for solving that long hairy equation I would start with replacing some of sub-expressions (like [imath](V+((L_2-1)\times p)[/imath] and all left hand side) by some new names, then reducing the fractions in the right hand side to a common denominator, etc.

As always, it would be easier to help you if you showed us what you have already tried and where do you feel you are stuck.
Click to expand...
Thank you very much for your reply.
I'm sorry for my poor explanation.
I'm not native English speaker and actually this is the first time I try to explain mathematic in English, please bear with me.
I will try to explain in details what I'm trying to achieve.

The purpose of my equation is to find the value which make 2 lines to cross each other.
The First Line (Line 1) is weighted moving average of Line 3 as below equation.
The Second Line (Line 2) is weighted moving average of different of 2 weighted moving average Lines (Line 3 & Line 4) in percentage as below equation.

1638751781269.png
1638751832843.png
1638751866475.png
1638751910266.png
 
1638751985289.png
Then I had tried to simplify it to

1638752029488.png

Currently I cannot figure out how to proceed next step to pull out my X from this current equation.
I will try your suggestion to replace some of sub-expressions to new simple name first.
If you have any other suggestion, please help me.
 
  • I still don't understand what problem you are solving. You say
  • The purpose of my equation is to find the value which make 2 lines to cross each other.
Click to expand...
  • but then you say "Line 1 = Line 2". Crossing and equality are different things -- which one do you need? Also which value do you need to find ? X and Y ? Something else?
  • How do you define Line 3 and Line 4 ? Is there an equation there ? Do you set those expressions to 0?
  • Are X and Y the variables in Line 3 and Line 4, and the rest of the names (like L1,L2, M, etc.) refer to some constant values ?
  • You mention that "D = previous value of Line 1" -- where does this previous value come from ? Is there an iterative process which you did not mention?

I do not believe I have a problem with your English (which is not my native language either), but with your math notation and statements. Can you describe some context for your problem? I.e., where does it come from? If this a homework from a textbook can you post a snapshot of the problem statement?
 
Hi blamocur, thanks again for your reply.
This is not a homework but real life problem.
I’m creating a trading system which utilize Average Direction Index (ADX) and Smoothen DI- crossover as a Sell Signal (wish you can understand what I say).
Equations for Line 1-4 is the function to calculate those data.
What I actually trying to find is variable “X” in the equation which represent “Low” price in candle stick data which will make ADX (Line 2) and Smoothen DI- (Line 1) to have “same value” (or crossing each other) which will then indicate my Sell Signal.
So I try to determine how much price have to move lower before my signal will appear by finding “X” from this equation.

For your other questions, I would like to reply as below.
  • How do you define Line 3 and Line 4 ? Is there an equation there ? Do you set those expressions to 0?
    Reply : Actually had already included in previous post which is equation for DI+ and DI- calculation and it’s expression is not 0.
  • Are X and Y the variables in Line 3 and Line 4, and the rest of the names (like L1,L2, M, etc.) refer to some constant values ?
    Reply : All names are not constant variable. Some of them are parameter (L1, L2, L3), some of them are value from other function (H, U, P, etc.) but I try to make it as simple as possible by giving a name to some of them which not include my X variable.
  • You mention that "D = previous value of Line 1" -- where does this previous value come from ? Is there an iterative process which you did not mention?
    Reply : Previous value can be calculate based on previous price information (from previous candle sticks) which is available (what I try to find is future price information from previous available data which will generate my signal).

    Hope you can understand what I’m trying to explain.
 
Last edited:
Hope you can understand what I’m trying to explain.
Click to expand...
Sorry, but I can't. Let me try to help you with your original post. As I understand it you need to solve the equation with one unknown X -- is this right?
 
Titanus said:
Hi, I’m new to this forum seeking your help to find the way to get final equation to derive “X” value.
I’ve tried my best to simplify my initial equation to the one posted below.
I’m struggling to pull out my X from function (X - Y) / (X + Y).
Any suggestion for next step to get my X ?
View attachment 30033
Click to expand...
The left hand side has an ambiguous part which I interpret as [imath]\left(L_1 - \frac{L_1}{L_3}\right)[/imath] -- is this correct ?
 
I’m struggling to pull out my X from function (X - Y) / (X + Y).
Click to expand...
I am assuming that "to pull out my X" means to express X through other values in an equation. If you have an equation [imath]\frac{X-Y}{X+Y} = Q[/imath] then [imath]X-Y = QX+QY[/imath], which can be transformed to [imath]X(1-Q) = (1+Q)Y[/imath] and get an expression for X : [imath]X = \frac{(1+Q)Y}{1-Q}[/imath].
Does this help?
 
blamocur said:
I am assuming that "to pull out my X" means to express X through other values in an equation. If you have an equation [imath]\frac{X-Y}{X+Y} = Q[/imath] then [imath]X-Y = QX+QY[/imath], which can be transformed to [imath]X(1-Q) = (1+Q)Y[/imath] and get an expression for X : [imath]X = \frac{(1+Q)Y}{1-Q}[/imath].
Does this help?
Click to expand...
This is the kind of answer I’m looking for... and yes I mean to express one unknown X through other values.
But with so many variables in the equation, I’m still struggling to simplify it to the form of X(1-Q) = (1-Q)Y.
Right now I’m trying to do as your previous suggestion to give names for sub-expresstions, It really did help to make it easier but still very complex for me ?.
I will try to do it first and if still struck at some point, I will let you know.

Anyway, thank you again for you help.
 
Last edited:
Titanus said:
This is the kind of answer I’m looking for... and yes I mean to express one unknown X through other values.
But with so many variables in the equation, I’m still struggling to simplify it to the form of X(1-Q) = (1-Q)Y.
Right now I’m trying to do as your previous suggestion to give names for sub-expresstions, It really did help to make it easier but still very complex for me ?.
I will try to do it first and if still struck at some point, I will let you know.

Anyway, thank you again for you help.
Click to expand...
You asked about [imath]\frac{X-Y}{X+Y}[/imath], but the actual expression in your first post is a difference of two fractions with different denominators, which can be transformed to a fraction with quadratic functions of X in both numerator and denominator. I.e., it will be more complicated than plain rational functions of X.
 
After trying hard and giving names to sub-expressions, I think I can simplify my equation down to below.
At this point I get struck again and have no idea how to get expression for just X.
Please help to give some suggestion how to solve this equation?
8088D60D-B490-42D7-A7BC-0679CAFF2D3A.jpeg
 
I’ve recognized that you had mention about quadratic function, so I just realized that I can arrange and solve my equation using it as below.
This the final answer to my question, isn’t it?
I cannot believe I can solve it finally...
871C8490-9EDE-49B9-A162-AEB2FB0C5D61.jpeg
 
blacamocur, thank you for your help!
After this will try to convert my equation into computer code and test that it working correctly or not (I really hope it will do).
 
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