#### Answer

There are two rational solutions.

#### Work Step by Step

$ 7x^{2}=19x\qquad$....add $-19x$ to each side to write in form of $ax^{2}+bx+c=0$.
$ 7x^{2}-19x=0\qquad$.... $a=7,\ b=-19,\ c=0$
$ b^{2}-4ac\qquad$....substitute $b$ for $-19,\ a$ for $7$ and $c$ for $0$
$=(-19)^{2}-4\cdot 7\cdot(0)$
$=361-0$
$=361$
Since the discriminant is a positive number that is a perfect square $(19^{2})$, there are two rational solutions.