Solve 3y^2-6y-x+1=0

$$3 y ^ { 2 } - 6 y - x + 1 = 0$$

Solve for x

$$x=3y^{2}-6y+1$$

Steps for Solving Linear Equation

Subtract 3y^{2} from both sides. Anything subtracted from zero gives its negation.

$$-6y-x+1=-3y^{2}$$

Add 6y to both sides.

$$-x+1=-3y^{2}+6y$$

Subtract 1 from both sides.

$$-x=-3y^{2}+6y-1$$

Divide both sides by -1.

$$\frac{-x}{-1}=\frac{-3y^{2}+6y-1}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x=\frac{-3y^{2}+6y-1}{-1}$$

Divide -3y^{2}+6y-1 by -1.

$$x=3y^{2}-6y+1$$

Solve for y (complex solution)

$$y=\frac{\sqrt{3x+6}}{3}+1$$

$$y=-\frac{\sqrt{3x+6}}{3}+1$$

Solve for y

$$y=\frac{\sqrt{3x+6}}{3}+1$$

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