Solve f=sqrt{9/f_{n*4pi^2*r}}

$$f = \sqrt { \frac { 9 } { f _ { n } \cdot 4 \pi ^ { 2 } \cdot r } }$$

Solve for f (complex solution)

$$f=\frac{3\left(f_{n}r\right)^{-\frac{1}{2}}}{2\pi }$$

$$f_{n}\neq 0\text{ and }r\neq 0$$

Solve for f_n (complex solution)

$$f_{n}=\frac{9}{4r\left(\pi f\right)^{2}}$$

$$r\neq 0\text{ and }arg(f)<\pi \text{ and }f\neq 0$$

Solve for f

$$f=\frac{3}{2\pi \sqrt{f_{n}r}}$$

$$\left(f_{n}<0\text{ and }r<0\right)\text{ or }\left(r>0\text{ and }f_{n}>0\right)$$

Solve for f_n

$$f_{n}=\frac{9}{4r\left(\pi f\right)^{2}}$$

$$f>0\text{ and }r\neq 0$$