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

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

Step 1

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

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

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

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

Step 4

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $4$ .

$x = \frac{- 12 \pm \sqrt{144 - 16 \cdot - 6}}{2 \cdot 4}$

Multiply $- 16$ by $- 6$ .

$x = \frac{- 12 \pm \sqrt{144 + 96}}{2 \cdot 4}$

Add $144$ and $96$ .

$x = \frac{- 12 \pm \sqrt{240}}{2 \cdot 4}$

Rewrite $240$ as $4^{2} \cdot 15$ .

Factor $16$ out of $240$ .

$x = \frac{- 12 \pm \sqrt{16 (15)}}{2 \cdot 4}$

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

$x = \frac{- 12 \pm \sqrt{4^{2} \cdot 15}}{2 \cdot 4}$

Pull terms out from under the radical.

$x = \frac{- 12 \pm 4 \sqrt{15}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{- 12 \pm 4 \sqrt{15}}{8}$

Simplify $\frac{- 12 \pm 4 \sqrt{15}}{8}$ .

$x = \frac{- 3 \pm \sqrt{15}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 3 \pm \sqrt{15}}{2}$

Decimal Form:

$x = 0.43649167 \dots, - 3.43649167 \dots$