[tex]2x^2-3x-2 \ \textgreater \ 0 \\\\ \hbox{Aflam radacinile inecuatiei de gradul II egaland ecuatia cu 0} \\\\ 2x^2-3x-2=0 \\\\ a=2 \\ b=-3\\c=-2 \\\\ \Delta=b^2-4ac \to(-3)^2-4*2*(-2)=9+16 \to \boxed{25} \\\\ x_1;x_2=\frac{-b\pm \sqrt{\Delta}}{2a}\to \frac{3\pm \sqrt{25}}{2*2}= \frac{3\pm 5}{4} \\\\\\ x_1=\frac{3+5}{4}= \frac{\not 8}{\not 4} \to \boxed{2} \\\\\\ x_2=\frac{3-5}{4}= \frac{-2}{4} \to \boxed{-\frac{1}{2}}[/tex]
[tex]\hbox{Facem tabelul semnelor:}[/tex]
x | -∞ [tex]-\frac{1}{2}[/tex] 2 +∞
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2x² -3x -2 |++++++++++ O ------ O ++++++++++
[tex]S \in (-\infty; -\frac{1}{2}) \cup (2; + \infty)[/tex]
