(2x − 5)(x + 2) = 18
$2x^2 - 5x + 4x - 10 - 18 = 0$
$2x^2 - x - 28 = 0$
$D = b^2 - 4ac = (-1)^2 - 4 * 2 * (-28) = 1 + 224 = 225 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{1 + \sqrt{225}}{2 * 2} = \frac{1 + 15}{4} = \frac{16}{4} = 4$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{1 - \sqrt{225}}{2 * 2} = \frac{1 - 15}{4} = \frac{-14}{4} = \frac{-7}{2} = -3,5$
Ответ: при x = −3,5 и x = 4

$(4x - 3)^2 + (3x - 1)(3x + 1) = 9$
$16x^2 - 24x + 9 + 9x^2 - 1 - 9 = 0$
$25x^2 - 24x - 1 = 0$
$D = b^2 - 4ac = (-24)^2 - 4 * 25 * (-1) = 576 + 100 = 676 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{24 + \sqrt{676}}{2 * 25} = \frac{24 + 26}{50} = \frac{50}{50} = 1$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{24 - \sqrt{676}}{2 * 25} = \frac{24 - 26}{50} = \frac{-2}{50} = -\frac{1}{25}$
Ответ: при $x = -\frac{1}{25}$ и x = 1

$(x + 3)^2 - (2x - 1)^2 = 16$
$x^2 + 6x + 9 - (4x^2 - 4x + 1) = 16$
$x^2 + 6x + 9 - 4x^2 + 4x - 1 - 16 = 0$
$-3x^2 + 10x - 8 = 0$
$D = b^2 - 4ac = 10^2 - 4 * (-3) * (-8) = 100 - 96 = 4 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-10 + \sqrt{4}}{2 * (-3)} = \frac{-10 + 2}{-6} = \frac{-8}{-6} = \frac{4}{3} = 1\frac{1}{3}$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-10 - \sqrt{4}}{2 * (-3)} = \frac{-10 - 2}{-6} = \frac{-12}{-6} = 2$
Ответ: при $x = 1\frac{1}{3}$ и x = 2

$(x - 6)^2 - 2x(x + 3) = 30 - 12x$
$x^2 - 12x + 36 - 2x^2 - 6x - 30 + 12x = 0$
$-x^2 - 6x + 6 = 0$
$D = b^2 - 4ac = (-6)^2 - 4 * (-1) * 6 = 36 + 24 = 60 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{6 + \sqrt{60}}{2 * (-1)} = \frac{6 + \sqrt{4 * 15}}{-2} = \frac{6 + 2\sqrt{15}}{-2} = -\frac{2(3 + \sqrt{15})}{2} = -3 - \sqrt{15}$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{6 - \sqrt{60}}{2 * (-1)} = \frac{6 - \sqrt{4 * 15}}{-2} = \frac{6 - 2\sqrt{15}}{-2} = -\frac{2(3 - \sqrt{15})}{2} = -3 + \sqrt{15}$
Ответ: при $x = -3 - \sqrt{15}$ и $x = -3 + \sqrt{15}$

(x + 7)(x − 8) − (4x + 1)(x − 2) = −21x
$x^2 + 7x - 8x - 56 - (4x^2 + x - 8x - 2) + 21x = 0$
$x^2 - x - 56 - 4x^2 - x + 8x + 2 + 21x = 0$
$-3x^2 + 27x - 54 = 0$ |: (−3)
$x^2 - 9x + 18 = 0$
$D = b^2 - 4ac = (-9)^2 - 4 * 1 * 18 = 81 - 72 = 9 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{9 + \sqrt{9}}{2 * 1} = \frac{9 + 3}{2} = \frac{12}{2} = 6$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{9 - \sqrt{9}}{2 * 1} = \frac{9 - 3}{2} = \frac{6}{2} = 3$
Ответ: при x = 3 и x = 6

(2x − 1)(2x + 1) − x(1 − x) = 2x(x + 1)
$4x^2 - 1 - x + x^2 = 2x^2 + 2x$
$5x^2 - x - 1 - 2x^2 - 2x = 0$
$3x^2 - 3x - 1 = 0$
$D = b^2 - 4ac = (-3)^2 - 4 * 3 * (-1) = 9 + 12 = 21 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{3 + \sqrt{21}}{2 * 3} = \frac{3 + \sqrt{21}}{6}$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{3 - \sqrt{21}}{2 * 3} = \frac{3 - \sqrt{21}}{6}$
Ответ: при $x = \frac{3 - \sqrt{21}}{6}$ и $x = \frac{3 + \sqrt{21}}{6}$