#### Answer

$x=\left\{ \dfrac{1}{5},4 \right\}$

#### Work Step by Step

Multiplying both sides by the $LCD=
6
$, then the solution to the given equation, $
\dfrac{5x^2}{6}-\dfrac{7x}{2}+\dfrac{2}{3}=0
$, is
\begin{array}{}
1(5x^2)-3(7x)+2(2)=6(0)
\\\\
5x^2-21x+4=0
\\\\
(5x-1)(x-4)=0
.\end{array}
Equating each factor to zero, then $
x=\left\{ \dfrac{1}{5},4 \right\}
$.