Question for the math wizzes:

Assume

0 < e < 1

0 < p < 1

g > 0

Is there a closed-form solution to the following equation?

p*x^(2+2*e) + g*(1-p)*x^2 - g*p*x^(2*e) - (1-p) = 0

I can find a numerical solution using Matlab, and it works just fine for my purposes, but I’m curious whether it has a closed-form solution.

It has such a “nice” look to it that I figure that there must be a way to re-arrange it and find a closed form solution to it.