# How do you solve 3x(x+2)=2 using the quadratic formula?

Jul 3, 2015

Convert the given equation to the form of a quadratic equation, $a {x}^{2} + b x + c = 0$. Identify a, b, and c. Substitute the values into the quadratic formula $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$, and solve for x. There will be two solutions for x.

#### Explanation:

The equation needs to be in the form $a {x}^{2} + b x + c = 0$.

$3 x \left(x + 2\right) = 2$

$3 {x}^{2} + 6 x = 2$

$3 {x}^{2} + 6 x - 2 = 0$

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

a=3;b=6;$c = - 2$

$x = \frac{- 6 \pm \sqrt{{6}^{2} - 4 \cdot 3 \cdot - 2}}{2 \cdot 3}$

$x = \frac{- 6 \pm \sqrt{36 + 24}}{6}$

$x = \frac{- 6 \pm \sqrt{60}}{6}$

$\sqrt{60} = \sqrt{4 \times 15} = 2 \sqrt{15}$

$x = \frac{- 6 \pm 2 \sqrt{15}}{6}$

$x = - 1 + \frac{2 \sqrt{15}}{3}$

$x = - 1 - \frac{2 \sqrt{15}}{3}$