Solve y=frac{sqrt{3x^2-4x-15}}{7-2x}

$$y = \frac{ \sqrt{ 3 { x }^{ 2 } -4x-15 } }{ 7-2x }$$

Solve for x

$$\left\{\begin{matrix}x=\frac{-14y^{2}-\sqrt{31y^{2}+49}+2}{3-4y^{2}}\text{, }&\left(y\geq 0\text{ and }y<\frac{\sqrt{3}}{2}\right)\text{ or }y<-\frac{\sqrt{3}}{2}\\x=\frac{-14y^{2}+\sqrt{31y^{2}+49}+2}{3-4y^{2}}\text{, }&y\neq \frac{\sqrt{3}}{2}\text{ and }y\geq 0\\x=\frac{207}{68}\approx 3.044117647\text{, }&y=\frac{\sqrt{3}}{2}\end{matrix}\right.$$

Solve for y

$$y=\frac{\sqrt{\left(x-3\right)\left(3x+5\right)}}{7-2x}$$

$$\left(x\geq 3\text{ and }x\neq \frac{7}{2}\right)\text{ or }x\leq -\frac{5}{3}$$