Solve Using the Quadratic Formula 4x^2+4x=15

$4 x^{2} + 4 x = 15$

Step 1

Subtract $15$ from both sides of the equation.

$4 x^{2} + 4 x - 15 = 0$

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 $a = 4$ , $b = 4$ , and $c = - 15$ into the quadratic formula and solve for $x$ .

$\frac{- 4 \pm \sqrt{4^{2} - 4 \cdot (4 \cdot - 15)}}{2 \cdot 4}$

Step 4

Simplify.

Simplify the numerator.

Raise $4$ to the power of $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 4 \cdot - 15}}{2 \cdot 4}$

Multiply $- 4 \cdot 4 \cdot - 15$ .

Multiply $- 4$ by $4$ .

$x = \frac{- 4 \pm \sqrt{16 - 16 \cdot - 15}}{2 \cdot 4}$

Multiply $- 16$ by $- 15$ .

$x = \frac{- 4 \pm \sqrt{16 + 240}}{2 \cdot 4}$

Add $16$ and $240$ .

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

Rewrite $256$ as $16^{2}$ .

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

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

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

Multiply $2$ by $4$ .

$x = \frac{- 4 \pm 16}{8}$

Simplify $\frac{- 4 \pm 16}{8}$ .

$x = \frac{- 1 \pm 4}{2}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{3}{2}, - \frac{5}{2}$