Solve Using the Quadratic Formula 6x^2=-12x-4

$6 x^{2} = - 12 x - 4$

Step 1

Move all the expressions to the left side of the equation.

Add $12 x$ to both sides of the equation.

$6 x^{2} + 12 x = - 4$

Add $4$ to both sides of the equation.

$6 x^{2} + 12 x + 4 = 0$

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 $a = 6$ , $b = 12$ , and $c = 4$ into the quadratic formula and solve for $x$ .

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

Step 4

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $6$ .

$x = \frac{- 12 \pm \sqrt{144 - 24 \cdot 4}}{2 \cdot 6}$

Multiply $- 24$ by $4$ .

$x = \frac{- 12 \pm \sqrt{144 - 96}}{2 \cdot 6}$

Subtract $96$ from $144$ .

$x = \frac{- 12 \pm \sqrt{48}}{2 \cdot 6}$

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$x = \frac{- 12 \pm \sqrt{16 (3)}}{2 \cdot 6}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{- 12 \pm \sqrt{4^{2} \cdot 3}}{2 \cdot 6}$

Pull terms out from under the radical.

$x = \frac{- 12 \pm 4 \sqrt{3}}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{- 12 \pm 4 \sqrt{3}}{12}$

Simplify $\frac{- 12 \pm 4 \sqrt{3}}{12}$ .

$x = \frac{- 3 \pm \sqrt{3}}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 3 \pm \sqrt{3}}{3}$

Decimal Form:

$x = - 0.42264973 \dots, - 1.57735026 \dots$