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

$12 x^{2} - 5 x - 2 = 0$

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 $a = 12$ , $b = - 5$ , and $c = - 2$ into the quadratic formula and solve for $x$ .

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

Step 3

Simplify.

Simplify the numerator.

Raise $- 5$ to the power of $2$ .

$x = \frac{5 \pm \sqrt{25 - 4 \cdot 12 \cdot - 2}}{2 \cdot 12}$

Multiply $- 4 \cdot 12 \cdot - 2$ .

Multiply $- 4$ by $12$ .

$x = \frac{5 \pm \sqrt{25 - 48 \cdot - 2}}{2 \cdot 12}$

Multiply $- 48$ by $- 2$ .

$x = \frac{5 \pm \sqrt{25 + 96}}{2 \cdot 12}$

Add $25$ and $96$ .

$x = \frac{5 \pm \sqrt{121}}{2 \cdot 12}$

Rewrite $121$ as $11^{2}$ .

$x = \frac{5 \pm \sqrt{11^{2}}}{2 \cdot 12}$

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

$x = \frac{5 \pm 11}{2 \cdot 12}$

Multiply $2$ by $12$ .

$x = \frac{5 \pm 11}{24}$

Step 4

The final answer is the combination of both solutions.

$x = \frac{2}{3}, - \frac{1}{4}$