[tex]|3x^2+5x-2|\leq 2\\
-2\leq 3x^2+5x-2\leq 2\\
i)-2\leq 3x^2+5x-2\\
3x^2+5x\geq0\\
x(3x+5)\geq 0\Rightarrow S_1=(-\infty ,-\frac{5}{3}]\cup [0,\infty)\\
ii)3x^2+5x-2\leq 2\\
3x^2+5x-4\leq 0\\
\Delta=25+48=73\Rightarrow \sqrt{\Delta}=\sqrt{73}\\
x_1=\frac{-5+\sqrt{73}}{6}\\
x_2=\frac{-5-\sqrt{73}}{6}}\\
S_2=[\frac{-5-\sqrt{73}}{6},\frac{-5+\sqrt{73}}{6}]\\
S=S_1\cap S_2=[\frac{-5-\sqrt{73}}{6},-\frac{5}{3}]\cup [0,\frac{\sqrt{73}-5}{6}]
[/tex]
