Solve x=sqrt{3y-1/2}

$$x = \sqrt { 3 y - \frac { 1 } { 2 } }$$

Solve for y

$$y=\frac{x^{2}}{3}+\frac{1}{6}$$

$$x\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{3y-\frac{1}{2}}=x$$

Square both sides of the equation.

$$3y-\frac{1}{2}=x^{2}$$

Add \frac{1}{2} to both sides of the equation.

$$3y-\frac{1}{2}-\left(-\frac{1}{2}\right)=x^{2}-\left(-\frac{1}{2}\right)$$

Subtracting -\frac{1}{2} from itself leaves 0.

$$3y=x^{2}-\left(-\frac{1}{2}\right)$$

Subtract -\frac{1}{2} from x^{2}.

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

Divide both sides by 3.

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

Dividing by 3 undoes the multiplication by 3.

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

Divide x^{2}+\frac{1}{2} by 3.

$$y=\frac{x^{2}}{3}+\frac{1}{6}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{12y-2}}{2}$$

Solve for y (complex solution)

$$y=\frac{x^{2}}{3}+\frac{1}{6}$$

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

Solve for x

$$x=\frac{\sqrt{12y-2}}{2}$$

$$y\geq \frac{1}{6}$$