# How do you solve using the quadratic formula 3x^2 + 4x = 6?

Mar 11, 2018

$x = \frac{- 4 \pm 2 \sqrt{22}}{6}$

#### Explanation:

The quadratic formula says that if we have a quadratic equation in the form:

$a {x}^{2} + b x + c = 0$

The solutions will be:
$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

In our case, we have to subtract $6$ from both sides to get it equal to $0$:

$3 {x}^{2} + 4 x - 6 = 0$

Now we can use the quadratic formula:
$x = \frac{- 4 \pm \sqrt{{\left(- 4\right)}^{2} - 4 \cdot 3 \cdot - 6}}{2 \cdot 3}$

$x = \frac{- 4 \pm \sqrt{16 - \left(- 72\right)}}{6}$

$x = \frac{- 4 \pm \sqrt{88}}{6} = \frac{- 4 \pm \sqrt{22 \cdot 4}}{6} = \frac{- 4 \pm 2 \sqrt{22}}{6}$