# Can this equation be solved?

#### gruebz

##### New member
Hi,

I've tried running this equation through algebra calculators but none of them seem to be able to solve it. I'm not sure if it's just too difficult for these calculators or if it's actually unsolvable.

I'm trying to solve for a:

c = (v * (a / b) ^ 5) + (w * (a / b) ^ 4) + (x * (a / b) ^ 3) + (y * (a / b) ^ 2) + (z * (a / b))

Any help is much appreciated.

Cheers
T

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi,

I've tried running this equation through algebra calculators but none of them seem to be able to solve it. I'm not sure if it's just too difficult for these calculators or if it's actually unsolvable.

I'm trying to solve for a:

c = (v * (a / b) ^ 5) + (w * (a / b) ^ 4) + (x * (a / b) ^ 3) + (y * (a / b) ^ 2) + (z * (a / b))

Any help is much appreciated.

Cheers
T
You have 8 variable s in the equation

Solve for which variable?

Solve for a

#### Dr.Peterson

##### Elite Member
I've tried running this equation through algebra calculators but none of them seem to be able to solve it. I'm not sure if it's just too difficult for these calculators or if it's actually unsolvable.

I'm trying to solve for a:

c = (v * (a / b) ^ 5) + (w * (a / b) ^ 4) + (x * (a / b) ^ 3) + (y * (a / b) ^ 2) + (z * (a / b))

Any help is much appreciated.
This is a fifth degree polynomial equation in the variable a; that is unsolvable except in particular cases (with specific numerical coefficients). See here: https://en.wikipedia.org/wiki/Quintic_function

Solving quintic equations in terms of radicals was a major problem in algebra from the 16th century, when cubic and quartic equations were solved, until the first half of the 19th century, when the impossibility of such a general solution was proved with the Abel–Ruffini theorem.​

#### JeffM

##### Elite Member
Hi,

I've tried running this equation through algebra calculators but none of them seem to be able to solve it. I'm not sure if it's just too difficult for these calculators or if it's actually unsolvable.

I'm trying to solve for a:

c = (v * (a / b) ^ 5) + (w * (a / b) ^ 4) + (x * (a / b) ^ 3) + (y * (a / b) ^ 2) + (z * (a / b))

Any help is much appreciated.

Cheers
T
This is a quintic equation in a/b. In general, quintic equations are not solvable by algebra. Of course, some specific cases can be solved exactly by algebra. And all cases can be solved by methods far more advanced than algebra.

Moreover, a good graphing system can give approximate solutions in all cases where b, c, v, w, x, y, and z are known constants.

#### gruebz

##### New member
Thanks... what about if I simplified to just trying to get the value of a/b

So I could rewrite this as:

Solve for a: c = (va5) + (wa4) + (xa3) + (ya2) + (za)

#### topsquark

##### Senior Member
Thanks... what about if I simplified to just trying to get the value of a/b

So I could rewrite this as:

Solve for a: c = (va5) + (wa4) + (xa3) + (ya2) + (za)
It's still a fifth order equation. As has already been pointed out there is no general method to solve such a thing in terms of arbitrary c, v, w, x, y, and z.

-Dan