Solucionar p=rq^2+2sq^2

$$p = r q ^ { 2 } + 2 s q ^ { 2 }$$

Resolver para q (solución compleja)

$$\left\{\begin{matrix}q=-\left(r+2s\right)^{-\frac{1}{2}}\sqrt{p}\text{; }q=\left(r+2s\right)^{-\frac{1}{2}}\sqrt{p}\text{, }&r\neq -2s\\q\in \mathrm{C}\text{, }&p=0\text{ and }r=-2s\end{matrix}\right,$$

Resolver para p

$$p=\left(r+2s\right)q^{2}$$

Resolver para q

$$\left\{\begin{matrix}q=\sqrt{\frac{p}{r+2s}}\text{; }q=-\sqrt{\frac{p}{r+2s}}\text{, }&\left(p\geq 0\text{ and }r>-2s\right)\text{ or }\left(p\leq 0\text{ and }r<-2s\right)\\q\in \mathrm{R}\text{, }&p=0\text{ and }r=-2s\end{matrix}\right,$$