Answer
There is one repeated rational solution.
Work Step by Step
$ 4x^{2}-12x+9=0\qquad$.... $a=4,\ b=-12,\ c=9$
$ b^{2}-4ac\qquad$....substitute $b$ for $-12,\ a$ for $4$ and $c$ for $9$
$=(-12)^{2}-4\cdot 4\cdot 9$
$=144-144$
$=0$
Since the discriminant equals $0$, there is one repeated rational solution.