$\frac{x^2 - 1}{2} - 11x = 11$ |*2
$x^2 - 1 - 22x = 22$
$x^2 - 22x - 23 = 0$
$D = 11^2 - 1 * (-23) = 144$
$x = 11 ± \sqrt{144} = 11 ± 12$
$x_1 = 11 - 12 = -1$
$x_2 = 11 + 12 = 23$
Ответ:
$x_1 = -1$;
$x_2 = 23$.

$\frac{x^2 + x}{2} = \frac{8x - 7}{3}$ |*6
$3(x^2 + x) = 2(8x - 7)$
$3x^2 + 3x = 16x - 14$
$3x^2 + 3x - 16x + 14 = 0$
$3x^2 - 13x + 14 = 0$
$D = 13^2 - 4 * 3 * 14 = 169 - 168 = 1$
$x = \frac{13 ± \sqrt{1}}{6}$
$x_1 = \frac{13 - 1}{6} = \frac{12}{6} = 2$
$x_2 = \frac{13 + 1}{6} = \frac{14}{6} = \frac{7}{3} = 2\frac{1}{3}$
Ответ:
$x_1 = 2$;
$x_2 = 2\frac{1}{3}$.

$\frac{4x^2 - 1}{3} = x(10x - 9)$ |3
$4x^2 - 1 = 30x^2 - 27x$
$4x^2 - 1 - 30x^2 + 27x = 0$
$-26x^2 + 27x - 1 = 0$ |(−1)
$26x^2 - 27x + 1 = 0$
$D = 27^2 - 4 * 26 * 1 = 729 - 104 = 625$
$x = \frac{27 ± \sqrt{625}}{52}$
$x_1 = \frac{27 - 25}{52} = \frac{2}{52} = \frac{1}{26}$
$x_2 = \frac{27 + 25}{52} = \frac{52}{52} = 1$
Ответ:
$x_1 = \frac{1}{26}$;
$x_2 = 1$.

$\frac{3}{4}x^2 - \frac{2}{5}x = \frac{4}{5}x^2 + \frac{3}{4}$ |*20
$15x^2 - 8x = 16x^2 + 15$
$16x^2 - 15x^2 + 8x + 15 = 0$
$x^2 + 8x + 15 = 0$
$D = 4^2 - 1 * 15 = 16 - 15 = 1$
$x = -4 ± \sqrt{1} = -4 ± 1$
$x_1 = -4 - 1 = -5$
$x_2 = -4 + 1 = -3$
Ответ:
$x_1 = -5$;
$x_2 = -3$.