Answer
The solution of the equation is $x=-\frac{1}{3},x=2$.
Work Step by Step
$\begin{align}
& 3{{x}^{2}}-5x=2 \\
& 3{{x}^{2}}-5x-2=0
\end{align}$
Factorize the equation,
$\begin{align}
& 3{{x}^{2}}-5x-2=0 \\
& 3{{x}^{2}}-6x+x-2=0 \\
& 3x\left( x-2 \right)+1\left( x-2 \right)=0 \\
& \left( 3x+1 \right)\left( x-2 \right)=0
\end{align}$
Set each factor equal to zero and solve:
$\begin{align}
& \left( 3x+1 \right)\left( x-2 \right)=0 \\
& \left( 3x+1 \right)=0\text{ or }\left( x-2 \right)=0 \\
& 3x=-1\text{ or }x=2
\end{align}$
Then,
$x=-\frac{1}{3},2$
