Answer
$x = \dfrac{-2 ± i \sqrt {2}}{3}$
Work Step by Step
Use the Quadratic Formula to find the solutions. The Quadratic Formula is given by:
$x = \dfrac{-b \pm \sqrt {b^2 - 4ac}}{2a}$, where $a$ is the coefficient of the squared term, $b$ is the coefficient of the linear term, and $c$ is the constant term.
In this exercise, $a = 3$, $b = 4$, and $c = 2$. Plug these values into the Quadratic Formula:
$x = \dfrac{-4 \pm \sqrt {4^2 - 4(3)(2)}}{2(3)}$
Simplify:
$\begin{align*}
x &= \dfrac{-4 \pm \sqrt {16 - 24}}{6}\\
x&= \frac{-4 \pm \sqrt {-8}}{6}
\end{align*}$
Rewrite the radicand as the product of perfect squares and another number:
$x = \dfrac{-4 \pm \sqrt {(-1)(4)(2)}}{6}$
Take the square roots of all perfect squares and use the fact the $\sqrt{-1}=i:$:
$x = \dfrac{-4 \pm 2i \sqrt {2}}{6}$
Divide both numerator and denominator by their greatest common factor, $2$:
$x = \dfrac{-2 \pm i \sqrt {2}}{3}$
