Answer
Since the discriminant is a positive number that is a perfect square ($10^{2}=100$), there are $2$ rational solutions.
Work Step by Step
$ 3x^{2}=4x+7\qquad$....add $-4x-7$ to both sides.
$ 3x^{2}-4x-7=0\qquad$.... $a=3,\ b=-4,\ c=-7$
$ b^{2}-4ac\qquad$....substitute $b$ for $-4,\ a$ for $3$ and $c$ for $-7$
$=(-4)^{2}-4\cdot(-7)\cdot 3$
$=16+84$
$=100$
