Solve y^2-6y-4x+21=0

$$y ^ { 2 } - 6 y - 4 x + 21 = 0$$

Solve for x

$$x=\frac{y^{2}-6y+21}{4}$$

Steps for Solving Linear Equation

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

$$-6y-4x+21=-y^{2}$$

Add 6y to both sides.

$$-4x+21=-y^{2}+6y$$

Subtract 21 from both sides.

$$-4x=-y^{2}+6y-21$$

Divide both sides by -4.

$$\frac{-4x}{-4}=\frac{-y^{2}+6y-21}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$x=\frac{-y^{2}+6y-21}{-4}$$

Divide -y^{2}+6y-21 by -4.

$$x=\frac{y^{2}}{4}-\frac{3y}{2}+\frac{21}{4}$$

Solve for y (complex solution)

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

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

Solve for y

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

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