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

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

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

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

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 24 \pm \sqrt{576 - 4 \cdot - 6 \cdot 0}}{2 \cdot - 6}$

Multiply $- 4 \cdot - 6 \cdot 0$ .

Multiply $- 4$ by $- 6$ .

$x = \frac{- 24 \pm \sqrt{576 + 24 \cdot 0}}{2 \cdot - 6}$

Multiply $24$ by $0$ .

$x = \frac{- 24 \pm \sqrt{576 + 0}}{2 \cdot - 6}$

Add $576$ and $0$ .

$x = \frac{- 24 \pm \sqrt{576}}{2 \cdot - 6}$

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

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

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

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

Multiply $2$ by $- 6$ .

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

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

$x = 2 \pm 2$

Step 4

The final answer is the combination of both solutions.

$x = 4, 0$