Answer
There are two rational solutions.
Work Step by Step
$ 5x^{2}=48x\qquad$....add $-48x$ to each side to write in form of $ax^{2}+bx+c=0$.
$ 5x^{2}-48x=0\qquad$.... $a=5,\ b=-48,\ c=0$
$ b^{2}-4ac\qquad$....substitute $b$ for $-48,\ a$ for $5$ and $c$ for $0$
$=(-48)^{2}-4\cdot 5\cdot(0)$
$=2304-0$
$=2304$
Since the discriminant is a positive number that is a perfect square $(48^{2})$, there are two rational solutions.