Solve ((x-7)^2+2)=6y

$$( ( x - 7 ) ^ { 2 } + 2 ) = 6 y$$

Solve for y

$$y=\frac{\left(x-7\right)^{2}+2}{6}$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-7\right)^{2}.

$$x^{2}-14x+49+2=6y$$

Add 49 and 2 to get 51.

$$x^{2}-14x+51=6y$$

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

$$6y=x^{2}-14x+51$$

Divide both sides by 6.

$$\frac{6y}{6}=\frac{x^{2}-14x+51}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$y=\frac{x^{2}-14x+51}{6}$$

Divide x^{2}-14x+51 by 6.

$$y=\frac{x^{2}}{6}-\frac{7x}{3}+\frac{17}{2}$$

Solve for x (complex solution)

$$x=-\sqrt{6y-2}+7$$

$$x=\sqrt{6y-2}+7$$

Solve for x

$$x=-\sqrt{6y-2}+7$$

$$x=\sqrt{6y-2}+7\text{, }y\geq \frac{1}{3}$$