Solve x=sqrt{4y-3}

$$x = \sqrt { 4 y - 3 }$$

Solve for y

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

$$x\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{4y-3}=x$$

Square both sides of the equation.

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

Add 3 to both sides of the equation.

$$4y-3-\left(-3\right)=x^{2}-\left(-3\right)$$

Subtracting -3 from itself leaves 0.

$$4y=x^{2}-\left(-3\right)$$

Subtract -3 from x^{2}.

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

Divide both sides by 4.

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

Dividing by 4 undoes the multiplication by 4.

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

Solve for y (complex solution)

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

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

Solve for x

$$x=\sqrt{4y-3}$$

$$y\geq \frac{3}{4}$$