How do I determine if an equation is solvable without solving it?

[Al-Layth]

Sometimes I come across equations with no closed form/analytic solution (trying to get it in the form x=) but I don't know until I try. How can I know if an Equation is solvable in this manner without actually solving it?

 

[Dr.Peterson]

Sometimes I come across equations with no closed form/analytic solution (trying to get it in the form x=) but I don't know until I try. How can I know if an Equation is solvable in this manner without actually solving it?

I'm not sure if there's a way to be certain when you see an unfamiliar equation, but when I see an equation with the unknown both inside and outside a transcendental function (e.g. x = sin(x), or x ln(x) = 5), I expect it to be unsolvable in closed form. Of course, there are other ways to be unsolvable, and many equations for which the solution is not merely "x = ...".)

 

[Al-Layth]

okay thx

 

[Steven G]

If you have x^2 = any negative number, then there is no real solution.
If |x| = any negative number, there is no solution.
If x^2 + y^2 = -23, there is no solution.
sin(x-pi) = 1.3 has no solution.
....

 

[Deleted member 4993]

If x^2 + y^2 = -23, there is no solution.

I assume you meant ........If x^2 + y^2 = -23, there is no real solution.

 

[Dr.Peterson]

sin(x-pi) = 1.3 has no solution.

I assume you meant, this has no real solution!

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