Solve x^2-(a+2)x+5a-6=0

$$x ^ { 2 } - ( a + 2 ) x + 5 a - 6 = 0$$

Solve for a

$$a=-\frac{x^{2}-2x-6}{5-x}$$

$$x\neq 5$$

Steps for Solving Linear Equation

Use the distributive property to multiply a+2 by x.

$$x^{2}-\left(ax+2x\right)+5a-6=0$$

To find the opposite of ax+2x, find the opposite of each term.

$$x^{2}-ax-2x+5a-6=0$$

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

$$-ax-2x+5a-6=-x^{2}$$

Add 2x to both sides.

$$-ax+5a-6=-x^{2}+2x$$

Add 6 to both sides.

$$-ax+5a=-x^{2}+2x+6$$

Combine all terms containing a.

$$\left(-x+5\right)a=-x^{2}+2x+6$$

The equation is in standard form.

$$\left(5-x\right)a=6+2x-x^{2}$$

Divide both sides by -x+5.

$$\frac{\left(5-x\right)a}{5-x}=\frac{6+2x-x^{2}}{5-x}$$

Dividing by -x+5 undoes the multiplication by -x+5.

$$a=\frac{6+2x-x^{2}}{5-x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{\left(a-14\right)\left(a-2\right)}+a+2}{2}$$

$$x=\frac{-\sqrt{\left(a-14\right)\left(a-2\right)}+a+2}{2}$$

Solve for x

$$x=\frac{\sqrt{\left(a-14\right)\left(a-2\right)}+a+2}{2}$$

$$x=\frac{-\sqrt{\left(a-14\right)\left(a-2\right)}+a+2}{2}\text{, }a\leq 2\text{ or }a\geq 14$$