Answer
$x=\left\{ -\dfrac{1}{6}, 3 \right\}$
Work Step by Step
Using properties of equality, the equation $
2x^2=\dfrac{17}{3}x+1
$ is equivalent to
\begin{array}{l}
6x^2=17x+3
\text{... multiply both sides by 3}
\\\\
6x^2-17x-3=0
\\\\
(6x+1)(x-3)=0
.\end{array}
Using the Zero Product Property, then $
x=\left\{ -\dfrac{1}{6}, 3 \right\}
$.
