Solve (y-6)^2=12(x-5)

$$( y - 6 ) ^ { 2 } = 12 ( x - 5 )$$

Solve for x

$$x=\frac{\left(y-6\right)^{2}+60}{12}$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-6\right)^{2}.

$$y^{2}-12y+36=12\left(x-5\right)$$

Use the distributive property to multiply 12 by x-5.

$$y^{2}-12y+36=12x-60$$

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

$$12x-60=y^{2}-12y+36$$

Add 60 to both sides.

$$12x=y^{2}-12y+36+60$$

Add 36 and 60 to get 96.

$$12x=y^{2}-12y+96$$

Divide both sides by 12.

$$\frac{12x}{12}=\frac{y^{2}-12y+96}{12}$$

Dividing by 12 undoes the multiplication by 12.

$$x=\frac{y^{2}-12y+96}{12}$$

Divide y^{2}-12y+96 by 12.

$$x=\frac{y^{2}}{12}-y+8$$

Solve for y (complex solution)

$$y=-2\sqrt{3x-15}+6$$

$$y=2\sqrt{3x-15}+6$$

Solve for y

$$y=-2\sqrt{3x-15}+6$$

$$y=2\sqrt{3x-15}+6\text{, }x\geq 5$$