Solve Using the Quadratic Formula 4x^2+12x=27

$4 x^{2} + 12 x = 27$

Step 1

Subtract $27$ from both sides of the equation.

$4 x^{2} + 12 x - 27 = 0$

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 $a = 4$ , $b = 12$ , and $c = - 27$ into the quadratic formula and solve for $x$ .

$\frac{- 12 \pm \sqrt{12^{2} - 4 \cdot (4 \cdot - 27)}}{2 \cdot 4}$

Step 4

Simplify.

Simplify the numerator.

Raise $12$ to the power of $2$ .

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot 4 \cdot - 27}}{2 \cdot 4}$

Multiply $- 4 \cdot 4 \cdot - 27$ .

Multiply $- 4$ by $4$ .

$x = \frac{- 12 \pm \sqrt{144 - 16 \cdot - 27}}{2 \cdot 4}$

Multiply $- 16$ by $- 27$ .

$x = \frac{- 12 \pm \sqrt{144 + 432}}{2 \cdot 4}$

Add $144$ and $432$ .

$x = \frac{- 12 \pm \sqrt{576}}{2 \cdot 4}$

Rewrite $576$ as $24^{2}$ .

$x = \frac{- 12 \pm \sqrt{24^{2}}}{2 \cdot 4}$

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

$x = \frac{- 12 \pm 24}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{- 12 \pm 24}{8}$

Simplify $\frac{- 12 \pm 24}{8}$ .

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

Step 5

The final answer is the combination of both solutions.

$x = \frac{3}{2}, - \frac{9}{2}$