Solve (2-m)x^2-8mx-m+5=0

$$( 2 - m ) x ^ { 2 } - 8 m x - m + 5 = 0$$

Solve for m (complex solution)

$$m=\frac{2x^{2}+5}{x^{2}+8x+1}$$

$$x\neq \sqrt{15}-4\text{ and }x\neq -\left(\sqrt{15}+4\right)$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2-m by x^{2}.

$$2x^{2}-mx^{2}-8mx-m+5=0$$

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

$$-mx^{2}-8mx-m+5=-2x^{2}$$

Subtract 5 from both sides.

$$-mx^{2}-8mx-m=-2x^{2}-5$$

Combine all terms containing m.

$$\left(-x^{2}-8x-1\right)m=-2x^{2}-5$$

Divide both sides by -x^{2}-8x-1.

$$\frac{\left(-x^{2}-8x-1\right)m}{-x^{2}-8x-1}=\frac{-2x^{2}-5}{-x^{2}-8x-1}$$

Dividing by -x^{2}-8x-1 undoes the multiplication by -x^{2}-8x-1.

$$m=\frac{-2x^{2}-5}{-x^{2}-8x-1}$$

Divide -2x^{2}-5 by -x^{2}-8x-1.

$$m=\frac{2x^{2}+5}{x^{2}+8x+1}$$

Solve for m

$$m=\frac{2x^{2}+5}{x^{2}+8x+1}$$

$$x\neq \sqrt{15}-4\text{ and }x\neq -\sqrt{15}-4$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2-m by x^{2}.

$$2x^{2}-mx^{2}-8mx-m+5=0$$

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

$$-mx^{2}-8mx-m+5=-2x^{2}$$

Subtract 5 from both sides.

$$-mx^{2}-8mx-m=-2x^{2}-5$$

Combine all terms containing m.

$$\left(-x^{2}-8x-1\right)m=-2x^{2}-5$$

Divide both sides by -x^{2}-8x-1.

$$\frac{\left(-x^{2}-8x-1\right)m}{-x^{2}-8x-1}=\frac{-2x^{2}-5}{-x^{2}-8x-1}$$

Dividing by -x^{2}-8x-1 undoes the multiplication by -x^{2}-8x-1.

$$m=\frac{-2x^{2}-5}{-x^{2}-8x-1}$$

Divide -2x^{2}-5 by -x^{2}-8x-1.

$$m=\frac{2x^{2}+5}{x^{2}+8x+1}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{15m^{2}+7m-10}+4m}{2-m}\text{; }x=\frac{-\sqrt{15m^{2}+7m-10}+4m}{2-m}\text{, }&m\neq 2\\x=\frac{3}{16}\text{, }&m=2\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{15m^{2}+7m-10}+4m}{2-m}\text{; }x=\frac{-\sqrt{15m^{2}+7m-10}+4m}{2-m}\text{, }&m\leq \frac{-\sqrt{649}-7}{30}\text{ or }\left(m\neq 2\text{ and }m\geq \frac{\sqrt{649}-7}{30}\right)\\x=\frac{3}{16}\text{, }&m=2\end{matrix}\right.$$