Solve 3yx^2-12x-1geq0

$$3y { x }^{ 2 } -12x-1 \geq 0$$

Solve for x

$$\left\{\begin{matrix}x\in [\frac{\sqrt{3}(\sqrt{y+12}+2\sqrt{3})}{3y},\infty)\cup (-\infty,-\frac{\sqrt{3(y+12)}-6}{3y}]\text{, }&y>0\\x\in [\frac{\sqrt{3}(\sqrt{y+12}+2\sqrt{3})}{3y},-\frac{\sqrt{3(y+12)}-6}{3y}]\text{, }&y>-12\text{ and }y<0\\x=-\frac{1}{6}\approx -0.166666667\text{, }&y\geq -12\text{ and }y\neq 0\\x\leq -\frac{1}{12}\text{, }&y\geq 0\end{matrix}\right.$$

Solve for y

$$y\geq \frac{12x+1}{3x^{2}}$$

$$x\neq 0$$