Answer
$\frac{- 4 + \sqrt{ 10} }{ 3}\approx -0.279$, $\frac{- 4 - \sqrt{ 10} }{ 3}\approx -2.387$
Work Step by Step
Given \begin{equation}
3 x^2+8 x=-2.
\end{equation}
Rearrange the equation before applying the quadratic formula and determine the constants $a$, $b$, $c$: \begin{equation}
\begin{aligned}
3 x^2+8 x&=-2\\
3 x^2+8 x+2&=0\\
ax^2+bx+c&=0\\
a =3, b= 8, c&= 2.
\end{aligned}
\end{equation} The quadratic formula gives: \begin{equation}
\begin{aligned}
x&=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\
n &==\frac{-8 \pm \sqrt{8^2-4 \cdot 3 \cdot 2}}{2 \cdot 3}\\
&=\frac{-8 \pm \sqrt{40} }{6}\\
&=\frac{-8 \pm \sqrt{4\cdot 10} }{6}\\
&=\frac{-2\cdot 4 \pm 2 \sqrt{ 10} }{2\cdot 3}\\
&=\frac{- 4 \pm \sqrt{ 10} }{\cdot 3}.
\end{aligned}
\end{equation} The solution is: \begin{equation}
x=\frac{- 4 + \sqrt{ 10} }{3}\approx -0.279 ,\quad x=\frac{- 4 - \sqrt{ 10} }{ 3}\approx -2.387.
\end{equation}
