Solve P(x)=3x^2-10x-6quadD(x)=x-3

$$P ( x ) = 3 x ^ { 2 } - 10 x - 6 \quad D ( x ) = x - 3$$

Solve for D

$$D=\frac{x}{2}-\frac{11}{6}+\frac{1}{2x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Subtract 3x^{2} from both sides.

$$-10x-6Dx=x-3-3x^{2}$$

Add 10x to both sides.

$$-6Dx=x-3-3x^{2}+10x$$

Combine x and 10x to get 11x.

$$-6Dx=11x-3-3x^{2}$$

The equation is in standard form.

$$\left(-6x\right)D=-3x^{2}+11x-3$$

Divide both sides by -6x.

$$\frac{\left(-6x\right)D}{-6x}=\frac{-3x^{2}+11x-3}{-6x}$$

Dividing by -6x undoes the multiplication by -6x.

$$D=\frac{-3x^{2}+11x-3}{-6x}$$

Divide 11x-3-3x^{2} by -6x.

$$D=\frac{x}{2}-\frac{11}{6}+\frac{1}{2x}$$

Solve for x (complex solution)

$$x=\frac{\sqrt{36D^{2}+132D+85}}{6}+D+\frac{11}{6}$$

$$x=-\frac{\sqrt{36D^{2}+132D+85}}{6}+D+\frac{11}{6}$$

Solve for x

$$x=\frac{\sqrt{36D^{2}+132D+85}}{6}+D+\frac{11}{6}$$

$$x=-\frac{\sqrt{36D^{2}+132D+85}}{6}+D+\frac{11}{6}\text{, }D\leq -\frac{17}{6}\text{ or }D\geq -\frac{5}{6}$$