Rearrangement of Zhang's Equation

Hello. I am having trouble rearranging this equation:

$\displaystyle Q=\frac{\pi t f_p f_m^2}{2(f_m^2 - f_p^2)}$

to get an equation for $\displaystyle f_p$ in terms of $\displaystyle t$. Only $\displaystyle f_p$ and $\displaystyle t$ are variables, the other symbols are constants.

I think I have got it as far as:

$\displaystyle \frac{f_p}{f_m^2}-\frac{1}{f_p}=\frac{-\pi t}{2Q}$

reasonably safely, but am not sure where to go from there! This looks distinctly like it should be quite do-able, but has been frustrating me all morning..

Any help would be appreciated.