Solve Using the Quadratic Formula 4x^2-2x-6=0

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

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 $a = 4$ , $b = - 2$ , and $c = - 6$ into the quadratic formula and solve for $x$ .

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

Step 3

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $4$ .

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

Multiply $- 16$ by $- 6$ .

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

Add $4$ and $96$ .

$x = \frac{2 \pm \sqrt{100}}{2 \cdot 4}$

Rewrite $100$ as $10^{2}$ .

$x = \frac{2 \pm \sqrt{10^{2}}}{2 \cdot 4}$

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

$x = \frac{2 \pm 10}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{2 \pm 10}{8}$

Simplify $\frac{2 \pm 10}{8}$ .

$x = \frac{1 \pm 5}{4}$

Step 4

The final answer is the combination of both solutions.

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