Solve Using the Quadratic Formula 3x^2-16x=12

$3 x^{2} - 16 x = 12$

Step 1

Subtract $12$ from both sides of the equation.

$3 x^{2} - 16 x - 12 = 0$

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 $a = 3$ , $b = - 16$ , and $c = - 12$ into the quadratic formula and solve for $x$ .

$\frac{16 \pm \sqrt{{(- 16)}^{2} - 4 \cdot (3 \cdot - 12)}}{2 \cdot 3}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 16$ to the power of $2$ .

$x = \frac{16 \pm \sqrt{256 - 4 \cdot 3 \cdot - 12}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 12$ .

Multiply $- 4$ by $3$ .

$x = \frac{16 \pm \sqrt{256 - 12 \cdot - 12}}{2 \cdot 3}$

Multiply $- 12$ by $- 12$ .

$x = \frac{16 \pm \sqrt{256 + 144}}{2 \cdot 3}$

Add $256$ and $144$ .

$x = \frac{16 \pm \sqrt{400}}{2 \cdot 3}$

Rewrite $400$ as $20^{2}$ .

$x = \frac{16 \pm \sqrt{20^{2}}}{2 \cdot 3}$

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

$x = \frac{16 \pm 20}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{16 \pm 20}{6}$

Simplify $\frac{16 \pm 20}{6}$ .

$x = \frac{8 \pm 10}{3}$

Step 5

The final answer is the combination of both solutions.

$x = 6, - \frac{2}{3}$