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

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

Solve for y

$$y=\left(x-2\right)\left(x-1\right)$$

Steps for Solving Linear Equation

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

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

Add 3x to both sides.

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

Subtract 2 from both sides.

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

Divide both sides by -1.

$$\frac{-y}{-1}=\frac{\left(1-x\right)\left(x-2\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$y=\frac{\left(1-x\right)\left(x-2\right)}{-1}$$

Divide \left(-2+x\right)\left(1-x\right) by -1.

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

Solve for x (complex solution)

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

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

Solve for x

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

$$x=\frac{-\sqrt{4y+1}+3}{2}\text{, }y\geq -\frac{1}{4}$$