here's another i can't solve.
t - 5√t - 14 = 0
i added 14 to both sides and then squared them. then i minused 196 and am left with t^2 + 15t -196 = 0
this doesn't work, what have i done wrong?
Notice it looks very much like a quadratic.
So use a dummy variable $\displaystyle x^2 = t$.
This would mean $\displaystyle x = \sqrt{t}$.
Your equation becomes
$\displaystyle x^2 - 5x - 14 = 0$
$\displaystyle (x - 7)(x + 2) = 0$
$\displaystyle x = -2$ or $\displaystyle x = 7$.
Note that, since $\displaystyle \sqrt{t} = x$, the solution $\displaystyle x = -2$ is unusable.
This means, since $\displaystyle t = x^2$, that $\displaystyle t = 49$.