$F=2F_{1}F_{2}+|F_{1}+F_{2}|$

$\left\{\begin{matrix}F_{1}=\frac{F-F_{2}}{2F_{2}+1}\text{, }&\left(F_{2}>-\frac{1}{2}\text{ or }F\leq -2F_{2}^{2}\right)\text{ and }\left(F_{2}<-\frac{1}{2}\text{ or }F\geq -2F_{2}^{2}\right)\text{ and }F_{2}\neq -\frac{1}{2}\\F_{1}\geq \frac{1}{2}\text{, }&F=-\frac{1}{2}\text{ and }F_{2}=-\frac{1}{2}\\F_{1}=-\frac{F+F_{2}}{1-2F_{2}}\text{, }&\left(F_{2}>\frac{1}{2}\text{ or }F\geq -2F_{2}^{2}\right)\text{ and }\left(F_{2}<\frac{1}{2}\text{ or }F\leq -2F_{2}^{2}\right)\text{ and }F_{2}\neq \frac{1}{2}\\F_{1}\leq -\frac{1}{2}\text{, }&F=-\frac{1}{2}\text{ and }F_{2}=\frac{1}{2}\end{matrix}\right.$