(possibly) unsolvable integral

Ok, so I was bored during AP Calculus after the test on integrals, and decided to entertain myself with a seemingly innocent math problem...

if you take a semi-circle represented by the equation

and divide the semi-circle into fourths, you end up with one-eight of a circle, with an area of

I want to know when the integral of the equation, represented by

from -R to X is equal to .

Basically, I need the following equation solved for X:

BTW, this problem will get me some SERIOUS extra credit points