Solve y=7sqrt{4x+12}-3

$$y=7 \sqrt{ 4x+12 } -3$$

Solve for x

$$x=\frac{\left(y+3\right)^{2}-588}{196}$$

$$\frac{y+3}{14}\geq 0$$

Steps for Solving Radical Equations

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

$$7\sqrt{4x+12}-3=y$$

Add 3 to both sides.

$$7\sqrt{4x+12}=y+3$$

Divide both sides by 7.

$$\frac{7\sqrt{4x+12}}{7}=\frac{y+3}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$\sqrt{4x+12}=\frac{y+3}{7}$$

Square both sides of the equation.

$$4x+12=\frac{\left(y+3\right)^{2}}{49}$$

Subtract 12 from both sides of the equation.

$$4x+12-12=\frac{\left(y+3\right)^{2}}{49}-12$$

Subtracting 12 from itself leaves 0.

$$4x=\frac{\left(y+3\right)^{2}}{49}-12$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{\frac{\left(y+3\right)^{2}}{49}-12}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{\frac{\left(y+3\right)^{2}}{49}-12}{4}$$

Divide \frac{\left(y+3\right)^{2}}{49}-12 by 4.

$$x=\frac{\left(y+3\right)^{2}}{196}-3$$

Solve for x (complex solution)

$$x=\frac{\left(y+3\right)^{2}-588}{196}$$

$$y=-3\text{ or }arg(\frac{y+3}{14})<\pi$$

Solve for y (complex solution)

$$y=14\sqrt{x+3}-3$$

Solve for y

$$y=14\sqrt{x+3}-3$$

$$x\geq -3$$