0\\\\ x_1*x_2 = \frac{-3}{2} = -3 * \frac{1}{2}\\\\ x_1 + x_2 = \frac{-5}{2} = \frac{1}{2} - 3\\\\ x_1 = -3, x_2 = \frac{1}{2}\\\\ x \in (-\infty,-3) \cup (\frac{1}{2}, +\infty)\\\\ 2x^2 + 5x - 3 = 2x - 1\\\\ 2x^2 + 3x - 2 = 0\\\\ x_1*x_2 = -1 = -2*\frac{1}{2}\\\\ x_1 + x_2 = -\frac{3}{2} = -2 + \frac{1}{2}\\\\ x_1 = -2, \ x_2 = \frac{1}{2}" alt="|2x^2 + 5x - 3| = 2x - 1\\\\ 2x - 1 \geq 0, 2x \geq 1, x \geq \frac{1}{2}\\\\ 1) \ 2x^2 + 5x - 3 > 0\\\\ x_1*x_2 = \frac{-3}{2} = -3 * \frac{1}{2}\\\\ x_1 + x_2 = \frac{-5}{2} = \frac{1}{2} - 3\\\\ x_1 = -3, x_2 = \frac{1}{2}\\\\ x \in (-\infty,-3) \cup (\frac{1}{2}, +\infty)\\\\ 2x^2 + 5x - 3 = 2x - 1\\\\ 2x^2 + 3x - 2 = 0\\\\ x_1*x_2 = -1 = -2*\frac{1}{2}\\\\ x_1 + x_2 = -\frac{3}{2} = -2 + \frac{1}{2}\\\\ x_1 = -2, \ x_2 = \frac{1}{2}" align="absmiddle" class="latex-formula">
![2) \ 2x^2 + 5x - 3 \leq 0\\\\ x \in [-3,\frac{1}{2}]\\\\ -2x^2 -5x + 3 = 2x - 1\\\\ -2x^2 - 7x + 4 = 0\\\\ x_1*x_2 = -2 = -4*\frac{1}{2}\\\\ x_1 + x_2 = -3.5 = -4 + \frac{1}{2}\\\\ x_1 = -4, \ \underline{x_2 = \frac{1}{2}}\\\\\\\\ \fbox{x = 0.5}](https://tex.z-dn.net/?f=2%29+%5C+2x%5E2+%2B+5x+-+3+%5Cleq+0%5C%5C%5C%5C+x+%5Cin+%5B-3%2C%5Cfrac%7B1%7D%7B2%7D%5D%5C%5C%5C%5C+-2x%5E2+-5x+%2B+3+%3D+2x+-+1%5C%5C%5C%5C+-2x%5E2+-+7x+%2B+4+%3D+0%5C%5C%5C%5C+x_1%2Ax_2+%3D+-2+%3D+-4%2A%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C+x_1+%2B+x_2+%3D+-3.5+%3D+-4+%2B+%5Cfrac%7B1%7D%7B2%7D%5C%5C%5C%5C+x_1+%3D+-4%2C+%5C+%5Cunderline%7Bx_2+%3D+%5Cfrac%7B1%7D%7B2%7D%7D%5C%5C%5C%5C%5C%5C%5C%5C+%5Cfbox%7Bx+%3D+0.5%7D "2) \ 2x^2 + 5x - 3 \leq 0\\\\ x \in [-3,\frac{1}{2}]\\\\ -2x^2 -5x + 3 = 2x - 1\\\\ -2x^2 - 7x + 4 = 0\\\\ x_1*x_2 = -2 = -4*\frac{1}{2}\\\\ x_1 + x_2 = -3.5 = -4 + \frac{1}{2}\\\\ x_1 = -4, \ \underline{x_2 = \frac{1}{2}}\\\\\\\\ \fbox{x = 0.5}")