Answer
The solution set is $(-\infty,-2]\cup[\frac{1}{2},\infty)$
Work Step by Step
$5x^2+3x\ge3x^2+2\hspace{0.7cm}{\color{blue}{\text{Given equation}}}$
$\Rightarrow 5x^2+3x-3x^2-2\ge0$
$\Rightarrow 2x^2+3x-2\ge0$
$\Rightarrow (2x-1)(x+2)\ge0\hspace{0.7cm}{\color{blue}{\text{Factor}}}$
The factors of the left-hand side are $2x-1$ and $x+2$.
These factors are zero when $x=\frac{1}{2}$ and $x=-2$.
These numbers divide the real line into the intervals
$(-\infty,-2),(-2,\frac{1}{2}),(\frac{1}{2},\infty)$
From the diagram and hence the inequality involves $\ge$, the endpoints of the intervals satisfy the inequality.
The solution set is $(-\infty,-2]\cup[\frac{1}{2},\infty)$
