$(x - 4)^2 = 4x - 11$
$x^2 - 8x + 16 - 4x + 11 = 0$
$x^2 - 12x + 27 = 0$
$D = b^2 - 4ac = (-12)^2 - 4 * 1 * 27 = 144 - 108 = 36 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{12 + \sqrt{36}}{2 * 1} = \frac{12 + 6}{2} = \frac{18}{2} = 9$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{12 - \sqrt{36}}{2 * 1} = \frac{12 - 6}{2} = \frac{6}{2} = 3$
Ответ: при x = 3 и x = 9

$(x + 5)^2 + (x - 7)(x + 7) = 6x - 19$
$x^2 + 10x + 25 + x^2 - 49 - 6x + 19 = 0$
$2x^2 + 4x - 5 = 0$
$D = b^2 - 4ac = 4^2 - 4 * 2 * (-5) = 16 + 40 = 56 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-4 + \sqrt{56}}{2 * 2} = \frac{-4 + \sqrt{4 * 14}}{4} = \frac{-4 + 2\sqrt{14}}{4} = \frac{2(-2 + \sqrt{14})}{4} = \frac{-2 + \sqrt{14}}{2}$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-4 - \sqrt{56}}{2 * 2} = \frac{-4 - \sqrt{4 * 14}}{4} = \frac{-4 - 2\sqrt{14}}{4} = \frac{2(-2 - \sqrt{14})}{4} = \frac{-2 - \sqrt{14}}{2}$
Ответ: при $x = \frac{-2 - \sqrt{14}}{2}$ и $x = \frac{-2 + \sqrt{14}}{2}$

(3x − 1)(x + 4) = (2x + 3)(x + 3) − 17
$3x^2 - x + 12x - 4 = 2x^2 + 3x + 6x + 9 - 17$
$3x^2 + 11x - 4 = 2x^2 + 9x - 8$
$3x^2 + 11x - 4 - 2x^2 - 9x + 8 = 0$
$x^2 + 2x + 4 = 0$
$D = b^2 - 4ac = 2^2 - 4 * 1 * 4 = 4 - 16 = -12 < 0$
Ответ: нет корней