Solve Using the Quadratic Formula 6x^2-8x-30=0

$6 x^{2} - 8 x - 30 = 0$

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 $a = 6$ , $b = - 8$ , and $c = - 30$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (6 \cdot - 30)}}{2 \cdot 6}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 6 \cdot - 30}}{2 \cdot 6}$

Multiply $- 4 \cdot 6 \cdot - 30$ .

Multiply $- 4$ by $6$ .

$x = \frac{8 \pm \sqrt{64 - 24 \cdot - 30}}{2 \cdot 6}$

Multiply $- 24$ by $- 30$ .

$x = \frac{8 \pm \sqrt{64 + 720}}{2 \cdot 6}$

Add $64$ and $720$ .

$x = \frac{8 \pm \sqrt{784}}{2 \cdot 6}$

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

$x = \frac{8 \pm \sqrt{28^{2}}}{2 \cdot 6}$

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

$x = \frac{8 \pm 28}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{8 \pm 28}{12}$

Simplify $\frac{8 \pm 28}{12}$ .

$x = \frac{2 \pm 7}{3}$

Step 4

The final answer is the combination of both solutions.

$x = 3, - \frac{5}{3}$