# How do you solve 3x^2=- 4x+2?

May 16, 2015

$3 {x}^{2} = - 4 x + 2$
can be re-arranged as
$3 {x}^{2} + 4 x - 2 = 0$

which has the general form
$a {x}^{2} + b x + c = 0$
with solutions given by the quadratic formula
$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

In this case
$x = \frac{- 4 \pm \sqrt{{4}^{2} - 4 \left(3\right) \left(- 2\right)}}{2 \left(3\right)}$

$x = \frac{- 2 \pm \sqrt{10}}{3}$