Solve y^2-4x-6y+1=0

$${ y }^{ 2 } -4x-6y+1=0$$

Solve for x

$$x=\frac{y^{2}-6y+1}{4}$$

Steps for Solving Linear Equation

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

$$-4x-6y+1=-y^{2}$$

Add 6y to both sides.

$$-4x+1=-y^{2}+6y$$

Subtract 1 from both sides.

$$-4x=-y^{2}+6y-1$$

Divide both sides by -4.

$$\frac{-4x}{-4}=\frac{-y^{2}+6y-1}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$x=\frac{-y^{2}+6y-1}{-4}$$

Divide -y^{2}+6y-1 by -4.

$$x=\frac{y^{2}}{4}-\frac{3y}{2}+\frac{1}{4}$$

Solve for y (complex solution)

$$y=2\sqrt{x+2}+3$$

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

Solve for y

$$y=2\sqrt{x+2}+3$$

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