Answer
$a.\quad x=-4.32,\ x=-1.12$ and $x=1.50$
$b.\quad x\in[-4.32,1.12]\cup[1.5,\infty)$
Work Step by Step
$a.$
Graph $f(x)=x^{3}+3x^{2}$ (red on the image)
and $g(x)=-x^{2}+3x+7$ (blue).
The solution (if it exists) is the x-coordinate of the intersection.
Solution: $x=-4.32,\ x=-1.12$ and $x=1.50$
$b.$
Using the graphs of part (a), we see that
the red graph is above or intersecting the blue graph on intervals
$[-4.32,1.12]\cup[1.5,\infty)$
