Question

$$- { x }^{ 2 } +(6-2z) \times -2 { z }^{ 2 } +z-3 < 0$$

Solve for x

$\left\{\begin{matrix}x\in \left(-\infty,-\sqrt{\left(z-3\right)\left(4z^{2}+1\right)}\right)\cup \left(\sqrt{\left(z-3\right)\left(4z^{2}+1\right)},\infty\right)\text{, }&z\geq 3\\x\in \mathrm{R}\text{, }&z<3\end{matrix}\right.$