## Intermediate Algebra (6th Edition)

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