Hi Zac,
Thanks for answering these questions :)
There is a couple of things here.
1) I think it should be $$10t^2+5t-2=0\qquad (NOT -5t)$$
2) I am not sure what the asker INTENDED the question to be BUT this was the question.
1/2+2/5t-1=1/5t+t
Technically this should be interpreted as
$$\\\frac{1}{2}+\frac{2}{5}t-1=\frac{1}{5}t+t\\\\
\frac{1}{2}+\frac{2t}{5}-1=\frac{1t}{5}+t\qquad $The t is on the top$\\\\
\frac{-1}{2}+\frac{2t}{5}=\frac{6t}{5}\\\\
\frac{-1}{2}=\frac{4t}{5}\\\\
\frac{-1*5}{2*4}=t\\\\
t=\frac{-5}{8}\\\\$$
Also, I would like you to consider putting in some blank lines.
Sometimes mine is spread out too much, I realize that, but I personally find it a bit hard to read when there are no spaces. This may just be a peronal preference. I am not sure :/