Solve Using the Quadratic Formula 8x^2-4x=24

$8 x^{2} - 4 x = 24$

Step 1

Subtract $24$ from both sides of the equation.

$8 x^{2} - 4 x - 24 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 8$ , $b = - 4$ , and $c = - 24$ into the quadratic formula and solve for $x$ .

$\frac{4 \pm \sqrt{{(- 4)}^{2} - 4 \cdot (8 \cdot - 24)}}{2 \cdot 8}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 4$ to the power of $2$ .

$x = \frac{4 \pm \sqrt{16 - 4 \cdot 8 \cdot - 24}}{2 \cdot 8}$

Multiply $- 4 \cdot 8 \cdot - 24$ .

Multiply $- 4$ by $8$ .

$x = \frac{4 \pm \sqrt{16 - 32 \cdot - 24}}{2 \cdot 8}$

Multiply $- 32$ by $- 24$ .

$x = \frac{4 \pm \sqrt{16 + 768}}{2 \cdot 8}$

Add $16$ and $768$ .

$x = \frac{4 \pm \sqrt{784}}{2 \cdot 8}$

Rewrite $784$ as $28^{2}$ .

$x = \frac{4 \pm \sqrt{28^{2}}}{2 \cdot 8}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{4 \pm 28}{2 \cdot 8}$

Multiply $2$ by $8$ .

$x = \frac{4 \pm 28}{16}$

Simplify $\frac{4 \pm 28}{16}$ .

$x = \frac{1 \pm 7}{4}$

Step 5

The final answer is the combination of both solutions.

$x = 2, - \frac{3}{2}$