Answer
There are two rational solutions.
Work Step by Step
$ 9t^{2}+3t=0\qquad$.... $a=9,\ b=3,\ c=0$
$ b^{2}-4ac\qquad$....substitute $b$ for $3,\ a$ for $9$ and $c$ for $0$
$=(3)^{2}-4\cdot 9\cdot(0)$
$=9+0$
$=9$
Since the discriminant is a positive number that is a perfect square, there are two rational solutions.