$19-2P=6F^{2}\text{ or }P=7$

$P=7$
$P=\frac{19}{2}-3F^{2}$

$\left\{\begin{matrix}F\in \mathrm{R}\text{, }&P=7\\F=-\frac{\sqrt{114-12P}}{6}\text{; }F=\frac{\sqrt{114-12P}}{6}\text{, }&P\leq \frac{19}{2}\end{matrix}\right.$