y=x(x-1)*500=500x^2-500x. The inverse of this formula has to have the form x=....
But this is a quadratic in x: 500x^2-500x-y=0.
It can also be written x^2-x=y/500.
Complete the square on the left-hand side: x^2-x+1/4=y/500+1/4, and because we had to add 1/4 to complete the square on the left, we must add the same value to the right.
(x-1/2)^2=y/500+1/4; x-1/2=±√(y/500+1/4), so x=1/2±√(y/500+1/4) gives us to solutions for x, one for the positive root and one for the negative.