Solve 2x^2-(m-4)x-48=0

$$2 x ^ { 2 } - ( m - 4 ) x - 48 = 0$$

Solve for m

$$m=2x+4-\frac{48}{x}$$

$$x\neq 0$$

Steps for Solving Linear Equation

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

$$2x^{2}-\left(mx-4x\right)-48=0$$

To find the opposite of mx-4x, find the opposite of each term.

$$2x^{2}-mx+4x-48=0$$

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

$$-mx+4x-48=-2x^{2}$$

Subtract 4x from both sides.

$$-mx-48=-2x^{2}-4x$$

Add 48 to both sides.

$$-mx=-2x^{2}-4x+48$$

The equation is in standard form.

$$\left(-x\right)m=48-4x-2x^{2}$$

Divide both sides by -x.

$$\frac{\left(-x\right)m}{-x}=\frac{2\left(4-x\right)\left(x+6\right)}{-x}$$

Dividing by -x undoes the multiplication by -x.

$$m=\frac{2\left(4-x\right)\left(x+6\right)}{-x}$$

Divide 2\left(4-x\right)\left(6+x\right) by -x.

$$m=2x+4-\frac{48}{x}$$

Solve for x

$$x=\frac{\sqrt{m^{2}-8m+400}+m-4}{4}$$

$$x=\frac{-\sqrt{m^{2}-8m+400}+m-4}{4}$$