Solve x^2+(2m-4)x+m-9=0

$$x ^ { 2 } + ( 2 m - 4 ) x + m - 9 = 0$$

Solve for m

$$m=-\frac{x^{2}-4x-9}{2x+1}$$

$$x\neq -\frac{1}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2m-4 by x.

$$x^{2}+2mx-4x+m-9=0$$

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

$$2mx-4x+m-9=-x^{2}$$

Add 4x to both sides.

$$2mx+m-9=-x^{2}+4x$$

Add 9 to both sides.

$$2mx+m=-x^{2}+4x+9$$

Combine all terms containing m.

$$\left(2x+1\right)m=-x^{2}+4x+9$$

The equation is in standard form.

$$\left(2x+1\right)m=9+4x-x^{2}$$

Divide both sides by 2x+1.

$$\frac{\left(2x+1\right)m}{2x+1}=\frac{9+4x-x^{2}}{2x+1}$$

Dividing by 2x+1 undoes the multiplication by 2x+1.

$$m=\frac{9+4x-x^{2}}{2x+1}$$

Solve for x

$$x=\sqrt{m^{2}-5m+13}-m+2$$

$$x=-\sqrt{m^{2}-5m+13}-m+2$$