Solve Using the Quadratic Formula 3x^2+12x=3

$3 x^{2} + 12 x = 3$

Step 1

Subtract $3$ from both sides of the equation.

$3 x^{2} + 12 x - 3 = 0$

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 $a = 3$ , $b = 12$ , and $c = - 3$ into the quadratic formula and solve for $x$ .

$\frac{- 12 \pm \sqrt{12^{2} - 4 \cdot (3 \cdot - 3)}}{2 \cdot 3}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot 3 \cdot - 3}}{2 \cdot 3}$

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

Multiply $- 4$ by $3$ .

$x = \frac{- 12 \pm \sqrt{144 - 12 \cdot - 3}}{2 \cdot 3}$

Multiply $- 12$ by $- 3$ .

$x = \frac{- 12 \pm \sqrt{144 + 36}}{2 \cdot 3}$

Add $144$ and $36$ .

$x = \frac{- 12 \pm \sqrt{180}}{2 \cdot 3}$

Rewrite $180$ as $6^{2} \cdot 5$ .

Factor $36$ out of $180$ .

$x = \frac{- 12 \pm \sqrt{36 (5)}}{2 \cdot 3}$

Rewrite $36$ as $6^{2}$ .

$x = \frac{- 12 \pm \sqrt{6^{2} \cdot 5}}{2 \cdot 3}$

Pull terms out from under the radical.

$x = \frac{- 12 \pm 6 \sqrt{5}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{- 12 \pm 6 \sqrt{5}}{6}$

Simplify $\frac{- 12 \pm 6 \sqrt{5}}{6}$ .

$x = - 2 \pm \sqrt{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - 2 \pm \sqrt{5}$

Decimal Form:

$x = 0.23606797 \dots, - 4.23606797 \dots$