Solve Using the Quadratic Formula 6x^2+12x+5=0

$6 x^{2} + 12 x + 5 = 0$

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 $a = 6$ , $b = 12$ , and $c = 5$ into the quadratic formula and solve for $x$ .

$\frac{- 12 \pm \sqrt{12^{2} - 4 \cdot (6 \cdot 5)}}{2 \cdot 6}$

Step 3

Simplify.

Simplify the numerator.

Raise $12$ to the power of $2$ .

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot 6 \cdot 5}}{2 \cdot 6}$

Multiply $- 4 \cdot 6 \cdot 5$ .

Multiply $- 4$ by $6$ .

$x = \frac{- 12 \pm \sqrt{144 - 24 \cdot 5}}{2 \cdot 6}$

Multiply $- 24$ by $5$ .

$x = \frac{- 12 \pm \sqrt{144 - 120}}{2 \cdot 6}$

Subtract $120$ from $144$ .

$x = \frac{- 12 \pm \sqrt{24}}{2 \cdot 6}$

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$x = \frac{- 12 \pm \sqrt{4 (6)}}{2 \cdot 6}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 12 \pm \sqrt{2^{2} \cdot 6}}{2 \cdot 6}$

Pull terms out from under the radical.

$x = \frac{- 12 \pm 2 \sqrt{6}}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{- 12 \pm 2 \sqrt{6}}{12}$

Simplify $\frac{- 12 \pm 2 \sqrt{6}}{12}$ .

$x = \frac{- 6 \pm \sqrt{6}}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 6 \pm \sqrt{6}}{6}$

Decimal Form:

$x = - 0.59175170 \dots, - 1.40824829 \dots$