Solve P(12)=x^2-mx+6=0

$$P ( 12 ) = x ^ { 2 } - m x + 6 = 0$$

Solve for m

$$m=x+\frac{6}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$-mx+6=-x^{2}$$

Subtract 6 from both sides.

$$-mx=-x^{2}-6$$

The equation is in standard form.

$$\left(-x\right)m=-x^{2}-6$$

Divide both sides by -x.

$$\frac{\left(-x\right)m}{-x}=\frac{-x^{2}-6}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$m=\frac{-x^{2}-6}{-x}$$

Divide -x^{2}-6 by -x.

$$m=x+\frac{6}{x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{m^{2}-24}+m}{2}$$

$$x=\frac{-\sqrt{m^{2}-24}+m}{2}$$

Solve for x

$$x=\frac{\sqrt{m^{2}-24}+m}{2}$$

$$x=\frac{-\sqrt{m^{2}-24}+m}{2}\text{, }|m|\geq 2\sqrt{6}$$