$\left\{\begin{matrix}x=\frac{\sqrt{p^{2}-4q\beta _{6}}-p}{2\beta _{6}}\text{; }x=-\frac{\sqrt{p^{2}-4q\beta _{6}}+p}{2\beta _{6}}\text{, }&\beta _{6}\neq 0\text{ and }a=\sqrt{19}\\x=-\frac{q}{p}\text{, }&\beta _{6}=0\text{ and }p\neq 0\text{ and }a=\sqrt{19}\\x\in \mathrm{C}\text{, }&\beta _{6}=0\text{ and }p=0\text{ and }q=0\text{ and }a=\sqrt{19}\end{matrix}\right.$

$\left\{\begin{matrix}x=\frac{\sqrt{p^{2}-4q\beta _{6}}-p}{2\beta _{6}}\text{; }x=-\frac{\sqrt{p^{2}-4q\beta _{6}}+p}{2\beta _{6}}\text{, }&\left(\beta _{6}\neq 0\text{ and }q\geq 0\text{ and }\beta _{6}\leq \frac{p^{2}}{4q}\text{ and }a=\sqrt{19}\right)\text{ or }\left(\beta _{6}\neq 0\text{ and }q=0\text{ and }a=\sqrt{19}\right)\text{ or }\left(\beta _{6}\neq 0\text{ and }\beta _{6}\geq \frac{p^{2}}{4q}\text{ and }q\leq 0\text{ and }a=\sqrt{19}\right)\text{ or }\left(p\neq 0\text{ and }\beta _{6}=\frac{p^{2}}{4q}\text{ and }q\neq 0\text{ and }a=\sqrt{19}\right)\\x=-\frac{q}{p}\text{, }&\beta _{6}=0\text{ and }p\neq 0\text{ and }a=\sqrt{19}\\x\in \mathrm{R}\text{, }&\beta _{6}=0\text{ and }p=0\text{ and }q=0\text{ and }a=\sqrt{19}\end{matrix}\right.$