1.
[tex]2x^{2}+2x-4 \geq 0\\\\a = 2, \ b = 2, \ c = -4\\\\\Delta =b^{2}-4ac = 2^{2}-4\cdot2\cdot(-4) = 4+32 = 36\\\\\sqrt{\Delta} = \sqrt{36} = 6\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-2-6}{2\cdot2}=\frac{-8}{4} = -2\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} =\frac{-2+6}{4} = \frac{4}{4} = 1[/tex]
a > 0, to parabola zwrócona jest ramionami do góry, wówczas:
[tex]\boxed{x \in(-\infty;-2\rangle \ \cup \ \langle1;+\infty)}[/tex]
2.
[tex]x^{2}\geq 9\\\\x^{2}-9 = 0\\\\(x+3)(x-3) = 0\\\\x+3 = 0 \ \vee \ x-3 = 0\\\\x = -3 \ \vee \ x = 3\\\\a > 0\\\\\boxed{x \in(-\infty;-3\rangle \ \cup \ \langle3;+\infty)}[/tex]
