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

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

Solve for y

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

Steps for Solving Linear Equation

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

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

Subtract 6x from both sides.

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

Subtract 1 from both sides.

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

Divide both sides by -4.

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

Dividing by -4 undoes the multiplication by -4.

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

Divide -x^{2}-6x-1 by -4.

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

Solve for x (complex solution)

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

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

Solve for x

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

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