Solve Using the Quadratic Formula 4x^2-11x-3=0

$4 x^{2} - 11 x - 3 = 0$

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 $a = 4$ , $b = - 11$ , and $c = - 3$ into the quadratic formula and solve for $x$ .

$\frac{11 \pm \sqrt{{(- 11)}^{2} - 4 \cdot (4 \cdot - 3)}}{2 \cdot 4}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 11$ to the power of $2$ .

$x = \frac{11 \pm \sqrt{121 - 4 \cdot 4 \cdot - 3}}{2 \cdot 4}$

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

Multiply $- 4$ by $4$ .

$x = \frac{11 \pm \sqrt{121 - 16 \cdot - 3}}{2 \cdot 4}$

Multiply $- 16$ by $- 3$ .

$x = \frac{11 \pm \sqrt{121 + 48}}{2 \cdot 4}$

Add $121$ and $48$ .

$x = \frac{11 \pm \sqrt{169}}{2 \cdot 4}$

Rewrite $169$ as $13^{2}$ .

$x = \frac{11 \pm \sqrt{13^{2}}}{2 \cdot 4}$

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

$x = \frac{11 \pm 13}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{11 \pm 13}{8}$

Step 4

The final answer is the combination of both solutions.

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