# How do you solve 3x² + 7x = -2?

Jun 28, 2015

By using the quadratic formula , you get $\left\{- 2 , - \frac{1}{3}\right\}$

#### Explanation:

The easiest way to solve a quadratic equation, is by using the quadratic formula. When you have a quadratic equation of the form
$a {x}^{2} + b x + c = 0$, you can find the solutions by using the equation:
$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

So first we need to convert your equation to that form:
3x^+7x=−2
$3 {x}^{2} + 7 x + 2 = 0$

So, in this case $a = 3 , b = 7$ and $c = 2$. If you fill this in in the quadratic formula, you get:

$x = \frac{- 7 \pm \sqrt{{7}^{2} - 4 \cdot 3 \cdot 2}}{2 \cdot 3}$

If you calculate it (once with a mins sign, once with a plus sign), you get:

${x}_{1} = - 2$
${x}_{2} = - \frac{1}{3}$