#### Answer

The equation has two rational solutions.

#### Work Step by Step

$3x^{2}+5x+2=0$
The discriminant is given by $b^{2}-4ac$. For this equation, $a=3$, $b=5$ and $c=2$
Let the discriminant be $D$. Substitute the known values into the formula and evaluate:
$D=5^{2}-4(3)(2)=25-24=1$
Since the discriminant is equal to a positive, perfect square number, the equation has two rational solutions and they are rational numbers.