Solve 3(y-1)^2=9x

$$3 ( y - 1 ) ^ { 2 } = 9 x$$

Solve for x

$$x=\frac{\left(y-1\right)^{2}}{3}$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(y-1\right)^{2}.

$$3\left(y^{2}-2y+1\right)=9x$$

Use the distributive property to multiply 3 by y^{2}-2y+1.

$$3y^{2}-6y+3=9x$$

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

$$9x=3y^{2}-6y+3$$

Divide both sides by 9.

$$\frac{9x}{9}=\frac{3\left(y-1\right)^{2}}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$x=\frac{3\left(y-1\right)^{2}}{9}$$

Divide 3\left(-1+y\right)^{2} by 9.

$$x=\frac{\left(y-1\right)^{2}}{3}$$

Solve for y (complex solution)

$$y=-\sqrt{3x}+1$$

$$y=\sqrt{3x}+1$$

Solve for y

$$y=-\sqrt{3x}+1$$

$$y=\sqrt{3x}+1\text{, }x\geq 0$$