663. Найдите корни уравнения: 1) (2x - 5)(x + 2) = 18; 2) (4x - 3)² + (3x-1)(3x + 1) = 9; 3) (x + 3)² - (2x - 1)² = 16; 4) (x - 6)² - 2x(x + 3) = 30 - 12x; 5) (x + 7)(x - 8) - (4x + 1)(x - 2) = -21x; 6) (2x - 1)(2x + 1) - x(1 - x) = 2x(x + 1).

663. 1) $$(2x - 5)(x + 2) = 18$$ $$2x^2 + 4x - 5x - 10 = 18$$ $$2x^2 - x - 28 = 0$$ $$D = (-1)^2 - 4 * 2 * (-28) = 1 + 224 = 225$$ $$x_1 = \frac{1 + \sqrt{225}}{4} = \frac{1 + 15}{4} = \frac{16}{4} = 4$$ $$x_2 = \frac{1 - \sqrt{225}}{4} = \frac{1 - 15}{4} = \frac{-14}{4} = -3.5$$ 2) $$(4x - 3)^2 + (3x-1)(3x + 1) = 9$$ $$16x^2 - 24x + 9 + 9x^2 - 1 = 9$$ $$25x^2 - 24x = 1$$ $$25x^2 - 24x - 1 = 0$$ $$D = (-24)^2 - 4 * 25 * (-1) = 576 + 100 = 676$$ $$x_1 = \frac{24 + \sqrt{676}}{50} = \frac{24 + 26}{50} = \frac{50}{50} = 1$$ $$x_2 = \frac{24 - \sqrt{676}}{50} = \frac{24 - 26}{50} = \frac{-2}{50} = -0.04$$ 3) $$(x + 3)^2 - (2x - 1)^2 = 16$$ $$x^2 + 6x + 9 - (4x^2 - 4x + 1) = 16$$ $$-3x^2 + 10x + 8 = 16$$ $$-3x^2 + 10x - 8 = 0$$ $$3x^2 - 10x + 8 = 0$$ $$D = (-10)^2 - 4 * 3 * 8 = 100 - 96 = 4$$ $$x_1 = \frac{10 + \sqrt{4}}{6} = \frac{10 + 2}{6} = \frac{12}{6} = 2$$ $$x_2 = \frac{10 - \sqrt{4}}{6} = \frac{10 - 2}{6} = \frac{8}{6} = \frac{4}{3}$$ 4) $$(x - 6)^2 - 2x(x + 3) = 30 - 12x$$ $$x^2 - 12x + 36 - 2x^2 - 6x = 30 - 12x$$ $$-x^2 - 6x + 6 = 0$$ $$x^2 + 6x - 6 = 0$$ $$D = 6^2 - 4 * 1 * (-6) = 36 + 24 = 60$$ $$x_1 = \frac{-6 + \sqrt{60}}{2} = \frac{-6 + 2\sqrt{15}}{2} = -3 + \sqrt{15}$$ $$x_2 = \frac{-6 - \sqrt{60}}{2} = \frac{-6 - 2\sqrt{15}}{2} = -3 - \sqrt{15}$$ 5) $$(x + 7)(x - 8) - (4x + 1)(x - 2) = -21x$$ $$x^2 - x - 56 - (4x^2 - 7x - 2) = -21x$$ $$-3x^2 + 6x - 54 = -21x$$ $$-3x^2 + 27x - 54 = 0$$ $$x^2 - 9x + 18 = 0$$ $$D = (-9)^2 - 4 * 1 * 18 = 81 - 72 = 9$$ $$x_1 = \frac{9 + \sqrt{9}}{2} = \frac{9 + 3}{2} = \frac{12}{2} = 6$$ $$x_2 = \frac{9 - \sqrt{9}}{2} = \frac{9 - 3}{2} = \frac{6}{2} = 3$$ 6) $$(2x - 1)(2x + 1) - x(1 - x) = 2x(x + 1)$$ $$4x^2 - 1 - x + x^2 = 2x^2 + 2x$$ $$5x^2 - x - 1 = 2x^2 + 2x$$ $$3x^2 - 3x - 1 = 0$$ $$D = (-3)^2 - 4 * 3 * (-1) = 9 + 12 = 21$$ $$x_1 = \frac{3 + \sqrt{21}}{6}$$ $$x_2 = \frac{3 - \sqrt{21}}{6}$$