Solve sqrt{f(x)}=-3/2x+105

$$\sqrt { f ( x ) } = \frac { - 3 } { 2 } x + 105$$

Solve for f

$$f=\frac{9\left(70-x\right)^{2}}{4x}$$

$$-\frac{3x}{2}+105\geq 0\text{ and }x\neq 0$$

Steps for Solving Radical Equations

Square both sides of the equation.

$$xf=\frac{9\left(70-x\right)^{2}}{4}$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{9\left(70-x\right)^{2}}{4x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{9\left(70-x\right)^{2}}{4x}$$

Solve for f (complex solution)

$$f=\frac{9\left(70-x\right)^{2}}{4x}$$

$$\left(x\neq 0\text{ and }arg(-\frac{3x}{2}+105)<\pi \right)\text{ or }x=70$$

Solve for x (complex solution)

$$x=\frac{2\left(-\sqrt{f\left(f+630\right)}+f+315\right)}{9}$$

$$x=\frac{2\left(\sqrt{f\left(f+630\right)}+f+315\right)}{9}\text{, }f=0\text{ or }arg(-\frac{3x}{2}+105)<\pi$$

Solve for x

$$\left\{\begin{matrix}x=\frac{2\left(\sqrt{f\left(f+630\right)}+f+315\right)}{9}\text{, }&f=0\text{ or }f\leq -630\\x=\frac{2\left(-\sqrt{f\left(f+630\right)}+f+315\right)}{9}\text{, }&f\leq -630\text{ or }f\geq 0\end{matrix}\right.$$