#### Answer

The equation has two rational solutions.

#### Work Step by Step

$8x^{2}=-14x-3$
Take all terms to the left side:
$8x^{2}+14x+3=0$
The discriminant is given by $b^{2}-4ac$. For this equation, $a=8$, $b=14$ and $c=3$
Let the discriminant be $D$. Substitute the known values into the formula and evaluate:
$D=14^{2}-4(8)(3)=196-96=100$
Since the discriminant is equal to a positive, perfect square number, the equation has two rational solutions and they are rational numbers.