#### Answer

The equation has two rational solutions.

#### Work Step by Step

$8x^{2}-72=0$
The discriminant is given by $b^{2}-4ac$. For this equation, $a=8$, $b=0$ and $c=-72$
Let the discriminant be $D$. Substitute the known values into the formula and evaluate:
$D=0^{2}-4(8)(-72)=2304$
Since the discriminant is equal to a positive, perfect square number, the equation has two solutions and they are rational numbers.