Answer
$$x∈(-\infty, -2) ∪ (0.5, +\infty)$$
Work Step by Step
$5x^2+3x\geq3x^2+2$
$5x^2+3x$ is represented as the Blue graph on the image above.
$3x^2+2$ is represented as the Red graph.
We have to locate the region where the Blue graph is above the Red graph. That is from $-\infty$ till $B$ and from $A$ to $+\infty$
$x∈(-\infty, -2) ∪ (0.5, +\infty)$