Solve for P (complex solution)
P=\sqrt{\frac{x+2w}{4x+3R}}
x\neq -\frac{3R}{4}
Solve for R (complex solution)
\left\{\begin{matrix}R=\frac{2w+x-4xP^{2}}{3P^{2}}\text{, }&x\neq -2w\text{ and }arg(P)<\pi \text{ and }P\neq 0\\R\neq \frac{8w}{3}\text{, }&P=0\text{ and }x=-2w\end{matrix}\right.
Solve for P
P=\sqrt{\frac{x+2w}{4x+3R}}
\left(x=-2w\text{ and }w\neq \frac{3R}{8}\right)\text{ or }\left(x\leq -2w\text{ and }x<-\frac{3R}{4}\right)\text{ or }\left(x\geq -2w\text{ and }x>-\frac{3R}{4}\right)
Solve for R
\left\{\begin{matrix}R=\frac{2w+x-4xP^{2}}{3P^{2}}\text{, }&P>0\text{ and }x\neq -2w\\R\neq \frac{8w}{3}\text{, }&x=-2w\text{ and }P=0\end{matrix}\right.
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