Solve Using the Quadratic Formula 3x^2+14x=-8

$3 x^{2} + 14 x = - 8$

Step 1

Add $8$ to both sides of the equation.

$3 x^{2} + 14 x + 8 = 0$

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 $a = 3$ , $b = 14$ , and $c = 8$ into the quadratic formula and solve for $x$ .

$\frac{- 14 \pm \sqrt{14^{2} - 4 \cdot (3 \cdot 8)}}{2 \cdot 3}$

Step 4

Simplify.

Simplify the numerator.

Raise $14$ to the power of $2$ .

$x = \frac{- 14 \pm \sqrt{196 - 4 \cdot 3 \cdot 8}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot 8$ .

Multiply $- 4$ by $3$ .

$x = \frac{- 14 \pm \sqrt{196 - 12 \cdot 8}}{2 \cdot 3}$

Multiply $- 12$ by $8$ .

$x = \frac{- 14 \pm \sqrt{196 - 96}}{2 \cdot 3}$

Subtract $96$ from $196$ .

$x = \frac{- 14 \pm \sqrt{100}}{2 \cdot 3}$

Rewrite $100$ as $10^{2}$ .

$x = \frac{- 14 \pm \sqrt{10^{2}}}{2 \cdot 3}$

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

$x = \frac{- 14 \pm 10}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{- 14 \pm 10}{6}$

Simplify $\frac{- 14 \pm 10}{6}$ .

$x = \frac{- 7 \pm 5}{3}$

Step 5

The final answer is the combination of both solutions.

$x = - \frac{2}{3}, - 4$