# How do you solve 3x^2 = -12x - 15?

Jan 17, 2016

$x = - 2 \pm i$

#### Explanation:

Move the terms to the same side of the equation.

$3 {x}^{2} + 12 x + 15 = 0$

Divide both sides by $3$.

${x}^{2} + 4 x + 5 = 0$

$x = \frac{- 4 \pm \sqrt{{4}^{2} - 4 \left(1\right) \left(5\right)}}{2}$

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

As you can now see, this equation only has complex (imaginary) roots.

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

$x = - 2 \pm i$