Solve x^2+4y-6x+3=0

$$x ^ { 2 } + 4 y - 6 x + 3 = 0$$

Solve for y

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

Steps for Solving Linear Equation

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

$$4y-6x+3=-x^{2}$$

Add 6x to both sides.

$$4y+3=-x^{2}+6x$$

Subtract 3 from both sides.

$$4y=-x^{2}+6x-3$$

Divide both sides by 4.

$$\frac{4y}{4}=\frac{-x^{2}+6x-3}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$y=\frac{-x^{2}+6x-3}{4}$$

Divide -x^{2}+6x-3 by 4.

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

Solve for x (complex solution)

$$x=\sqrt{6-4y}+3$$

$$x=-\sqrt{6-4y}+3$$

Solve for x

$$x=\sqrt{6-4y}+3$$

$$x=-\sqrt{6-4y}+3\text{, }y\leq \frac{3}{2}$$