If I understood it right then this is a way to solve it
\(\frac{5}{2t}-t=3+\frac{3}{2t} | t\neq 0 \\ \\ 5-2t^2 = 3t+3 \\ 2t^2+3t-2=0 |\textrm{ QE}\\ \textrm{Put it in the quadratic formula:} \\ t_{1,2}=\frac{-3\pm \sqrt{9+16}}{4}=\frac{-3\pm 5}{4}\\ \underline{\underline{t_{1}=\frac{1}{2} | t_{2}=-2}}\)
