Solve x=sqrt{2y+4div3}

$$x= \sqrt{ 2y+4 \div 3 }$$

Solve for y

$$y=\frac{x^{2}}{2}-\frac{2}{3}$$

$$x\geq 0$$

Steps for Solving Radical Equations

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{2y+\frac{4}{3}}=x$$

Square both sides of the equation.

$$2y+\frac{4}{3}=x^{2}$$

Subtract \frac{4}{3} from both sides of the equation.

$$2y+\frac{4}{3}-\frac{4}{3}=x^{2}-\frac{4}{3}$$

Subtracting \frac{4}{3} from itself leaves 0.

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

Divide both sides by 2.

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

Dividing by 2 undoes the multiplication by 2.

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

Divide x^{2}-\frac{4}{3} by 2.

$$y=\frac{x^{2}}{2}-\frac{2}{3}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{18y+12}}{3}$$

Solve for y (complex solution)

$$y=\frac{x^{2}}{2}-\frac{2}{3}$$

$$arg(x)<\pi \text{ or }x=0$$

Solve for x

$$x=\frac{\sqrt{18y+12}}{3}$$

$$y\geq -\frac{2}{3}$$