Question

$$\zeta(x)=2\frac{3}{x+2}+1;x_{1}=-2,x_{2}=-z$$

Solve for x (complex solution)

$\left\{\begin{matrix}x=\frac{\sqrt{4\zeta ^{2}+28\zeta +1}-2\zeta +1}{2\zeta }\text{; }x=\frac{-\sqrt{4\zeta ^{2}+28\zeta +1}-2\zeta +1}{2\zeta }\text{, }&\zeta \neq 0\text{ and }x_{1}=-2\text{ and }x_{2}=-z\\x=-8\text{, }&\zeta =0\text{ and }x_{1}=-2\text{ and }x_{2}=-z\end{matrix}\right.$

Solve for x

$\left\{\begin{matrix}x=\frac{\sqrt{4\zeta ^{2}+28\zeta +1}-2\zeta +1}{2\zeta }\text{; }x=\frac{-\sqrt{4\zeta ^{2}+28\zeta +1}-2\zeta +1}{2\zeta }\text{, }&\zeta \neq 0\text{ and }\left(\zeta \geq 2\sqrt{3}-\frac{7}{2}\text{ or }\zeta \leq -2\sqrt{3}-\frac{7}{2}\right)\text{ and }x_{2}=-z\text{ and }x_{1}=-2\\x=-8\text{, }&\zeta =0\text{ and }x_{1}=-2\text{ and }x_{2}=-z\end{matrix}\right.$