Solve 4y=sqrt{4x+9}

$$4 y = \sqrt { 4 x + 9 }$$

Solve for y (complex solution)

$$y=\frac{\sqrt{4x+9}}{4}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$4y=\sqrt{4x+9}$$

Divide both sides by 4.

$$\frac{4y}{4}=\frac{\sqrt{4x+9}}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$y=\frac{\sqrt{4x+9}}{4}$$

Solve for x

$$x=4y^{2}-\frac{9}{4}$$

$$y\geq 0$$

Steps for Solving Radical Equations

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

$$\sqrt{4x+9}=4y$$

Square both sides of the equation.

$$4x+9=16y^{2}$$

Subtract 9 from both sides of the equation.

$$4x+9-9=16y^{2}-9$$

Subtracting 9 from itself leaves 0.

$$4x=16y^{2}-9$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{16y^{2}-9}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{16y^{2}-9}{4}$$

Divide 16y^{2}-9 by 4.

$$x=4y^{2}-\frac{9}{4}$$

Solve for y

$$y=\frac{\sqrt{4x+9}}{4}$$

$$x\geq -\frac{9}{4}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$4y=\sqrt{4x+9}$$

Divide both sides by 4.

$$\frac{4y}{4}=\frac{\sqrt{4x+9}}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$y=\frac{\sqrt{4x+9}}{4}$$

Solve for x (complex solution)

$$x=4y^{2}-\frac{9}{4}$$

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