Solve Using the Quadratic Formula 6x^2-24=0

$6 x^{2} - 24 = 0$

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 $a = 6$ , $b = 0$ , and $c = - 24$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (6 \cdot - 24)}}{2 \cdot 6}$

Step 3

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 6 \cdot - 24}}{2 \cdot 6}$

Multiply $- 4 \cdot 6 \cdot - 24$ .

Multiply $- 4$ by $6$ .

$x = \frac{0 \pm \sqrt{0 - 24 \cdot - 24}}{2 \cdot 6}$

Multiply $- 24$ by $- 24$ .

$x = \frac{0 \pm \sqrt{0 + 576}}{2 \cdot 6}$

Add $0$ and $576$ .

$x = \frac{0 \pm \sqrt{576}}{2 \cdot 6}$

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

$x = \frac{0 \pm \sqrt{24^{2}}}{2 \cdot 6}$

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

$x = \frac{0 \pm 24}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{0 \pm 24}{12}$

Simplify $\frac{0 \pm 24}{12}$ .

$x = \pm 2$

Step 4

The final answer is the combination of both solutions.

$x = 2, - 2$