Решите уравнение |2x^2+5x-3|=2x-1

  [latex]|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}[/latex]     [latex]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}[/latex]