$5x^2 = 9x + 2$
$5x^2 - 9x - 2 = 0$
$D = 9^2 - 4 * 5 * (-2) = 81 + 40 = 121$
$x = \frac{9 ± \sqrt{121}}{10}$
$x_1 = \frac{9 - 11}{10} = \frac{-2}{10} = -0,2$
$x_2 = \frac{9 + 11}{10} = \frac{20}{10} = 2$
Ответ:
$x_1 = -0,2$;
$x_2 = 2$.

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

$6x + 9 = x^2$
$x^2 - 6x - 9 = 0$
$D = 3^2 - 1 * (-9) = 18 = (3\sqrt{2})^2$
$x = 3 ± 3\sqrt{2}$

$z - 5 = z^2 - 25$
$z^2 - 25 - z + 5 = 0$
$z^2 - z - 20 = 0$
$D = 1^2 - 4 * 1 * (-20) = 1 + 80 = 81$
$z = \frac{1 ± \sqrt{81}}{2}$
$z_1 = \frac{1 - 9}{2} = \frac{-8}{2} = -4$
$z_2 = \frac{1 + 9}{2} = \frac{10}{2} = 5$
Ответ:
$z_1 = -4$;
$z_2 = 5$.

$y^2 = 52y - 576$
$y^2 - 52y + 576 = 0$
$D = 26^2 - 1 * 576 = 676 - 576 = 100$
$y = \frac{26 ± \sqrt{100}}{1}$
$y_1 = \frac{26 - 10}{1} = 16$
$y_2 = \frac{26 + 10}{1} = 36$
Ответ:
$y_1 = 16$;
$y_2 = 36$.

$15y^2 - 30 = 22y + 7$
$15y^2 - 30 - 22y - 7 = 0$
$15y^2 - 22y - 37 = 0$
$D = 11^2 - 15 * (-37) = 121 + 555 = 676$
$y = \frac{11 ± \sqrt{676}}{15}$
$y_1 = \frac{11 - 26}{15} = \frac{-15}{15} = -1$
$y_2 = \frac{11 + 26}{15} = \frac{37}{15} = 2\frac{7}{15}$
Ответ:
$y_1 = -1$;
$y_2 = 2\frac{7}{15}$.

$25p^2 = 10p - 1$
$25p^2 - 10p + 1 = 0$
$D = 5^2 - 25 * 1 = 25 - 25 = 0$
$p = \frac{5}{25} = \frac{1}{5}$

$299x^2 + 100x = 500 - 101x^2$
$299x^2 + 100x - 500 + 101x^2 = 0$
$400x^2 + 100x - 500 = 0$ |:100
$4x^2 + x - 5 = 0$
$D = 1^2 - 4 * 4 * (-5) = 1 + 80 = 81$
$x = \frac{-1 ± \sqrt{81}}{8}$
$x_1 = \frac{-1 - 9}{8} = \frac{-10}{8} = -\frac{5}{4} = -1,25$
$x_2 = \frac{-1 + 9}{8} = \frac{8}{8} = 1$
Ответ:
$x_1 = -1,25$;
$x_2 = 1$.