#### Answer

$x=\left\{ \dfrac{2}{5},-\dfrac{1}{2} \right\}$

#### Work Step by Step

Multiplying both sides by the $LCD=
20
$, then the solution to the given equation, $
\dfrac{x^2}{2}+\dfrac{x}{20}=\dfrac{1}{10}
$, is
\begin{array}{}
10(x^2)+1(x)=2(1)
\\\\
10x^2+x=2
\\\\
10x^2+x-2=0
\\\\
(5x-2)(2x+1)=0
.\end{array}
Equating each factor to zero, then $
x=\left\{ \dfrac{2}{5},-\dfrac{1}{2} \right\}
$.