(x − 4)(x + 2) − 2(3x + 1)(x − 3) = x(x + 27)
$x^2 - 4x + 2x - 8 - 2(3x^2 + x - 9x - 3) = x^2 + 27x$
$x^2 - 2x - 8 - 6x^2 - 2x + 18x + 6 - x^2 - 27x = 0$
$-6x^2 - 13x - 2 = 0$ | * (−1)
$6x^2 + 13x + 2 = 0$
$D = b^2 - 4ac = 13^2 - 4 * 6 * 2 = 169 - 48 = 121 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-13 + \sqrt{121}}{2 * 6} = \frac{-13 + 11}{12} = \frac{-2}{12} = -\frac{1}{6}$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-13 - \sqrt{121}}{2 * 6} = \frac{-13 - 11}{12} = \frac{-24}{12} = -2$
Ответ: −2 и $-\frac{1}{6}$

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

$(x + 4)(x^2 + x - 13) - (x + 7)(x^2 + 2x - 5) = x + 1$
$x^3 + x^2 - 13x + 4x^2 + 4x - 52 - (x^3 + 2x^2 - 5x + 7x^2 + 14x - 35) - x - 1 = 0$
$x^3 + 5x^2 - 9x - 52 - x^3 - 2x^2 + 5x - 7x^2 - 14x + 35 - x - 1 = 0$
$-4x^2 - 19x - 18 = 0$ | * (−1)
$4x^2 + 19x + 18 = 0$
$D = b^2 - 4ac = 19^2 - 4 * 4 * 18 = 361 - 288 = 73 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-19 + \sqrt{73}}{2 * 4} = \frac{-19 + \sqrt{73}}{8}$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-19 - \sqrt{73}}{2 * 4} = \frac{-19 - \sqrt{73}}{8}$
Ответ: $\frac{-19 - \sqrt{73}}{8}$ и $\frac{-19 + \sqrt{73}}{8}$

$\frac{2(x^2 - 9)}{5} - \frac{x + 1}{2} = \frac{x - 41}{4}$ | * 20
$4 * 2(x^2 - 9) - 10(x + 1) = 5(x - 41)$
$8x^2 - 72 - 10x - 10 = 5x - 205$
$8x^2 - 10x - 82 - 5x + 205 = 0$
$8x^2 - 15x + 123 = 0$
$D = b^2 - 4ac = (-15)^2 - 4 * 8 * 123 = 225 - 3936 = -3711 < 0$
Ответ: нет корней

$\frac{x^2 + 5x}{3} - \frac{x + 3}{2} = \frac{2x^2 - 2}{8}$ | * 24
$8(x^2 + 5x) - 12(x + 3) = 3(2x^2 - 2)$
$8x^2 + 40x - 12x - 36 = 6x^2 - 6$
$8x^2 + 28x - 36 - 6x^2 + 6 = 0$
$2x^2 + 28x - 30 = 0$ | : 2
$x^2 + 14x - 15 = 0$
$D = b^2 - 4ac = 14^2 - 4 * 1 * (-15) = 196 + 60 = 256 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-14 + \sqrt{256}}{2 * 1} = \frac{-14 + 16}{2} = \frac{2}{2} = 1$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-14 - \sqrt{256}}{2 * 1} = \frac{-14 - 16}{2} = \frac{-30}{2} = -15$
Ответ: −15 и 1