# Solution of quantile function

Find the quantile function of $$q=F(x)=[(1-\exp(-bx))^c]*[1+d-d*(1-\exp(-bx))^c]$$ , where $b, c$ are positive real and $-1<d<1$. Its answer is

Any help/hint is most welcome.

Take the term in the first square bracket, call it $z$, then you have a quadratic in $z$. Solve for $z$ then it is easy to solve for $x$. The 2d is in the wrong place in your solution, just a type I guess. Not sure why just one root of the quadratic is used. Also think about what happens when d<0.