Solve y=sqrt{5x+4}

$$y = \sqrt { 5 x + 4 }$$

Solve for x

$$x=\frac{y^{2}-4}{5}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{5x+4}=y$$

Square both sides of the equation.

$$5x+4=y^{2}$$

Subtract 4 from both sides of the equation.

$$5x+4-4=y^{2}-4$$

Subtracting 4 from itself leaves 0.

$$5x=y^{2}-4$$

Divide both sides by 5.

$$\frac{5x}{5}=\frac{y^{2}-4}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$x=\frac{y^{2}-4}{5}$$

Solve for x (complex solution)

$$x=\frac{y^{2}-4}{5}$$

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

Solve for y

$$y=\sqrt{5x+4}$$

$$x\geq -\frac{4}{5}$$