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

May 27, 2016

$1.721$ and $- .387$

#### Explanation:

First you want to get all of the variable on the same side

$3 {x}^{2} - 4 x = 2$

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

Remember that $a {x}^{2} + b x + c = 0$ so $a = 3$, $b = - 4$, and $c = - 2$

${x}_{1 , 2} = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

so

${x}_{1 , 2} = \frac{- \left(- 4\right) \pm \sqrt{{\left(- 4\right)}^{2} - 4 \left(3\right) \left(- 2\right)}}{2 \left(3\right)}$

${x}_{1 , 2} = \frac{4 \pm \sqrt{16 + 24}}{6}$

${x}_{1 , 2} = \frac{4 \pm \sqrt{40}}{6}$

Since $\sqrt{40} = 6.325$ (rounded), sub that in and add/subtract according to the equation

$\frac{4 + 6.325}{6} = 1.721$

$\frac{4 - 6.325}{6} = - .387$