#### Answer

$t=\left\{ -\dfrac{1}{2},\dfrac{3}{4} \right\}$

#### Work Step by Step

Multiplying both sides by the $LCD=
10
$, then the solution to the given equation, $
\dfrac{4t^2}{5}=\dfrac{t}{5}+\dfrac{3}{10}
$, is
\begin{array}{}
2(4t^2)=2(t)+1(3)
\\\\
8t^2=2t+3
\\\\
8t^2-2t-3=0
\\\\
(2t+1)(4t-3)=0
.\end{array}
Equating each factor to zero, then $
t=\left\{ -\dfrac{1}{2},\dfrac{3}{4} \right\}
$.