Answer
There are two rational solutions.
Work Step by Step
$ 4m^{2}+7m=0\qquad$.... $a=4,\ b=7,\ c=0$
$ b^{2}-4ac\qquad$....substitute $b$ for $7,\ a$ for $4$ and $c$ for $0$
$=(7)^{2}-4\cdot 4\cdot(0)$
$=49+0$
$=49$
Since the discriminant is a positive number that is a perfect square, there are two rational solutions.