# Math Help - Rearrangement of Zhang's Equation

1. ## Rearrangement of Zhang's Equation

Hello. I am having trouble rearranging this equation:

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

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

I think I have got it as far as:

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

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.

2. Originally Posted by stealthbadger
Hello. I am having trouble rearranging this equation:

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

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

I think I have got it as far as:

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

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.
Streamline things a bit:

$Q = \frac{A f_p}{B - f_p^2}$

and it should be obvious what the constants A and B represent.

Then:

$QB - Qf_p^2 = A f_p \Rightarrow Q f_p^2 + A f_p - QB = 0$.

Solve the quadratic for $f_p$ and then substitute the appropriate expressions for A and B.

3. I did this initially, but $t$ is not a constant, so I didn't think that it was valid?

4. Originally Posted by stealthbadger
I did this initially, but $t$ is not a constant, so I didn't think that it was valid?
It is.