Solve x^2+y-4x-6y+10=0

$$x ^ { 2 } + y - 4 x - 6 y + 10 = 0$$

Solve for y

$$y=\frac{x^{2}-4x+10}{5}$$

Steps for Solving Linear Equation

Combine y and -6y to get -5y.

$$x^{2}-5y-4x+10=0$$

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

$$-5y-4x+10=-x^{2}$$

Add 4x to both sides.

$$-5y+10=-x^{2}+4x$$

Subtract 10 from both sides.

$$-5y=-x^{2}+4x-10$$

Divide both sides by -5.

$$\frac{-5y}{-5}=\frac{-x^{2}+4x-10}{-5}$$

Dividing by -5 undoes the multiplication by -5.

$$y=\frac{-x^{2}+4x-10}{-5}$$

Divide -x^{2}+4x-10 by -5.

$$y=\frac{x^{2}}{5}-\frac{4x}{5}+2$$

Solve for x (complex solution)

$$x=\sqrt{5y-6}+2$$

$$x=-\sqrt{5y-6}+2$$

Solve for x

$$x=\sqrt{5y-6}+2$$

$$x=-\sqrt{5y-6}+2\text{, }y\geq \frac{6}{5}$$