[tex]2x^{2}+5x+2 = 0\\\\a = 2, \ b = 5, \ c = 2\\\\\Delta = b^{2}-4ac = 5^{2} -4\cdot2\cdot2 = 25 - 16 = 9\\\\\Sqrt{\Delta = \sqrt{9} = 3[/tex]
[tex]x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-5-3}{2\cdot2} = \frac{-8}{4} = -2\\\\x_2=\frac{-b+\sqrt{\Delta}}{2a} = \frac{-5+3}{4} = \frac{-2}{4} = -\frac{1}{2}\\\\x\in \{-2, -\frac{1}{2}\}[/tex]
