Answer
$2$ solutions if $48\gt c$, one solution if $48=c$, and no solution if $4\lt x$.
Work Step by Step
The discriminant is $D=b^2-4ac$. If $D\gt0$ we have $2$, if $D=0$ we have one, and if $D\lt0$ we have no solution.
Hence here $D=576-12c$. $576-12c\gt0\\576\gt12c\\48\gt c.$
$576-12c=0\\576=12c\\48= c.$8
$576-12c\lt0\\576\lt12c\\48\lt c.$
Thus we have $2$ solutions if $48\gt c$, one solution if $48=c$, and no solution if $4\lt x$.
