$2x^2 - 5x - 3 = 0$
$D = 5^2 - 4 * 2 * (-3) = 25 + 24 = 49$
$x = \frac{5 ± \sqrt{49}}{4}$
$x_1 = \frac{5 - 7}{4} = \frac{-2}{4} = -0,5$
$x_2 = \frac{5 + 7}{4} = \frac{12}{4} = 3$
Ответ:
$x_1 = -0,5$;
$x_2 = 3$.

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

$5x^2 + 9x + 4 = 0$
$D = 9^2 - 4 * 5 * 4 = 81 - 80 = 1$
$x = \frac{-9 ± \sqrt{1}}{10}$
$x_1 = \frac{-9 - 1}{10} = \frac{-10}{10} = -1$
$x_2 = \frac{-9 + 1}{10} = \frac{-8}{10} = -0,8$
Ответ:
$x_1 = -1$;
$x_2 = -0,8$.

$36y^2 - 12y + 1 = 0$
$D = 6^2 - 36 * 1 = 36 - 36 = 0$
$y = \frac{6}{36} = \frac{1}{6}$

$3t^2 - 3t + 1 = 0$
$D = 3^2 - 4 * 3 * 1 = 9 - 12 = -3 < 0$
Уравнение не имеет корней.

$x^2 + 9x - 22 = 0$
$D = 9^2 - 4 * 1 * (-22) = 81 + 88 = 169$
$x = \frac{-9 ± \sqrt{169}}{2}$
$x_1 = \frac{-9 - 13}{2} = \frac{-22}{2} = -11$
$x_2 = \frac{-9 + 13}{2} = \frac{4}{2} = 2$
Ответ:
$x_1 = -11$;
$x_2 = 2$.

$y^2 - 12y + 32 = 0$
$D = 6^2 - 1 * 32 = 36 - 32 = 4$
$y = \frac{6 ± \sqrt{4}}{1}$
$y_1 = \frac{6 - 2}{1} = 4$
$y_2 = \frac{6 + 2}{1} = 8$
Ответ:
$y_1 = 4$;
$y_2 = 8$.

$100x^2 - 160x + 63 = 0$
$D = 80^2 - 100 * 63 = 6400 - 6300 = 100$
$x = \frac{80 ± \sqrt{100}}{100}$
$x_1 = \frac{80 - 10}{100} = \frac{70}{100} = 0,7$
$x_2 = \frac{80 + 10}{100} = \frac{90}{100} = 0,9$
Ответ:
$x_1 = 0,7$;
$x_2 = 0,9$.