Question

$$\left. \begin{array} { l } { g g 3 x ^ { 2 } + 6 x + 12 = 0 , } \\ { \frac { a f } { \sqrt { a \right.$$

Solve for x (complex solution)

$\left\{\begin{matrix}x=\frac{\sqrt{3\left(3-4gg_{3}\right)}-3}{gg_{3}}\text{; }x=-\frac{\sqrt{3}\left(\sqrt{3-4gg_{3}}+\sqrt{3}\right)}{gg_{3}}\text{, }&g_{3}\neq 0\text{ and }g\neq 0\\x=-2\text{, }&g_{3}=0\text{ or }g=0\end{matrix}\right.$

Solve for x

$\left\{\begin{matrix}x=\frac{\sqrt{3\left(3-4gg_{3}\right)}-3}{gg_{3}}\text{; }x=-\frac{\sqrt{3}\left(\sqrt{3-4gg_{3}}+\sqrt{3}\right)}{gg_{3}}\text{, }&\left(g\neq 0\text{ and }g\leq \frac{3}{4g_{3}}\text{ and }g_{3}>0\right)\text{ or }\left(g\neq 0\text{ and }g\geq \frac{3}{4g_{3}}\text{ and }g_{3}<0\right)\text{ or }\left(g=\frac{3}{4g_{3}}\text{ and }g_{3}\neq 0\right)\\x=-2\text{, }&g_{3}=0\text{ or }g=0\end{matrix}\right.$