$14x^2 - 5x - 1 = 0$
$D = 5^2 - 4 * 14 * (-1) = 25 + 56 = 81$
$x = \frac{5 ± \sqrt{81}}{2 * 14}$
$x_1 = \frac{5 - 9}{2 * 14} = \frac{-4}{28} = -\frac{1}{7}$
$x_2 = \frac{5 + 9}{2 * 14} = \frac{14}{28} = \frac{1}{2}$
Ответ:
$x_1 = -\frac{1}{7}$;
$x_2 = \frac{1}{2}$.

$-y^2 + 3y + 5 = 0$ |*(−1)
$y^2 - 3y - 5 = 0$
$D = 3^2 - 4 * 1 * (-5) = 9 + 20 = 29$
$y = \frac{3 ± \sqrt{29}}{2}$

$2x^2 + x + 67 = 0$
$D = 1^2 - 4 * 2 * 67 = 1 - 536 = -535 < 0$
Уравнение не имеет корней

$1 - 18p + 81p^2 = 0$
$81p^2 - 18p + 1 = 0$
$D = 18^2 - 4 * 81 * 1 = 324 - 324 = 0$
$p = \frac{18}{2 * 81} = \frac{9}{1 * 81} = \frac{1}{9}$

$-11y + y^2 - 152 = 0$
$y^2 - 11y - 152 = 0$
$D = 11^2 - 4 * 1 * (-152) = 121 + 608 = 729$
$y = \frac{11 ± \sqrt{729}}{2}$
$y_1 = \frac{11 - 27}{2} = \frac{-16}{2} = -8$
$y_2 = \frac{11 + 27}{2} = \frac{38}{2} = 19$
Ответ:
$y_1 = -8$;
$y_2 = 19$.

$18 + 3x^2 - x = 0$
$3x^2 - x + 18 = 0$
$D = 1^2 - 4 * 3 * 18 = 1 - 216 = -215 < 0$
Уравнение не имеет корней