Answer
$x=\dfrac{2-\sqrt{10}}{3}
\text{ and }
x=\dfrac{2+\sqrt{10}}{3}
$
Work Step by Step
Using the properties of equality, the given equation, $
3x^2=2(2x+1)
,$ is equivalent to
\begin{align*}
3x^2&=2(2x)+2(1)
&\text{ (use Distributive Property)}
\\
3x^2&=4x+2
\\
3x^2-4x-2&=0
\end{align*}
In the equation above, $a=
3
,$ $b=
-4
,$ and $c=
-2
.$
Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then
\begin{align*}\require{cancel}x&=
\dfrac{-(-4)\pm\sqrt{(-4)^2-4(3)(-2)}}{2(3)}
\\\\&=
\dfrac{4\pm\sqrt{16+24}}{6}
\\\\&=
\dfrac{4\pm\sqrt{40}}{6}
\\\\&=
\dfrac{4\pm\sqrt{4\cdot10}}{6}
\\\\&=
\dfrac{4\pm2\sqrt{10}}{6}
\\\\&=
\dfrac{\cancel4^2\pm\cancel2^1\sqrt{10}}{\cancel6^3}
&\text{ (divide by $2$)}
\\\\&=
\dfrac{2\pm\sqrt{10}}{3}
\end{align*}
Hence, the solutions are $
x=\dfrac{2-\sqrt{10}}{3}
\text{ and }
x=\dfrac{2+\sqrt{10}}{3}
.$