Solve n=2pq/sqrt{m-3}

$$n = \frac { 2 p q } { \sqrt { m - 3 } }$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=4\times \left(\frac{pq}{n}\right)^{2}+3\text{, }&|arg(n\sqrt{\left(\frac{pq}{n}\right)^{2}})-arg(pq)|<\pi \text{ and }q\neq 0\text{ and }p\neq 0\text{ and }n\neq 0\\m\neq 3\text{, }&\left(p=0\text{ or }q=0\right)\text{ and }n=0\end{matrix}\right.$$

Solve for n (complex solution)

$$n=2\left(m-3\right)^{-\frac{1}{2}}pq$$

$$m\neq 3$$

Solve for m

$$\left\{\begin{matrix}m=4\times \left(\frac{pq}{n}\right)^{2}+3\text{, }&\left(n>0\text{ and }q>0\text{ and }p>0\right)\text{ or }\left(n>0\text{ and }p<0\text{ and }q<0\right)\text{ or }\left(n<0\text{ and }p<0\text{ and }q>0\right)\text{ or }\left(n<0\text{ and }q<0\text{ and }p>0\right)\\m>3\text{, }&\left(n=0\text{ and }p=0\right)\text{ or }\left(n=0\text{ and }q=0\right)\end{matrix}\right.$$

Solve for n

$$n=\frac{2pq}{\sqrt{m-3}}$$

$$m>3$$