Solve Using the Quadratic Formula 3x^2-24x-48=0

$3 x^{2} - 24 x - 48 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 3$ , $b = - 24$ , and $c = - 48$ into the quadratic formula and solve for $x$ .

$\frac{24 \pm \sqrt{{(- 24)}^{2} - 4 \cdot (3 \cdot - 48)}}{2 \cdot 3}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 24$ to the power of $2$ .

$x = \frac{24 \pm \sqrt{576 - 4 \cdot 3 \cdot - 48}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 48$ .

Multiply $- 4$ by $3$ .

$x = \frac{24 \pm \sqrt{576 - 12 \cdot - 48}}{2 \cdot 3}$

Multiply $- 12$ by $- 48$ .

$x = \frac{24 \pm \sqrt{576 + 576}}{2 \cdot 3}$

Add $576$ and $576$ .

$x = \frac{24 \pm \sqrt{1152}}{2 \cdot 3}$

Rewrite $1152$ as $24^{2} \cdot 2$ .

Factor $576$ out of $1152$ .

$x = \frac{24 \pm \sqrt{576 (2)}}{2 \cdot 3}$

Rewrite $576$ as $24^{2}$ .

$x = \frac{24 \pm \sqrt{24^{2} \cdot 2}}{2 \cdot 3}$

Pull terms out from under the radical.

$x = \frac{24 \pm 24 \sqrt{2}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{24 \pm 24 \sqrt{2}}{6}$

Simplify $\frac{24 \pm 24 \sqrt{2}}{6}$ .

$x = 4 \pm 4 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 4 \pm 4 \sqrt{2}$

Decimal Form:

$x = 9.65685424 \dots, - 1.65685424 \dots$