$x^2 - 2x - 5 = 0$
$D = 1^2 + 5 = 1 + 5 = 6$
$x_{1,2} = 1 ± \sqrt{6}$
Проверка:
$(1 - \sqrt{6})^2 - 2(1 - \sqrt{6}) - 5 = 1 - 2\sqrt{6} + 6 - 2 + 2\sqrt{6} - 5 = 0$
$(1 + \sqrt{6})^2 - 2(1 + \sqrt{6}) - 5 = 1 + 2\sqrt{6} + 6 - 2 - 2\sqrt{6} - 5 = 0$

$x^2 + 4x + 1 = 0$
$D = 2^2 - 1 = 4 - 1 = 3$
$x_{1,2} = -2 ± \sqrt{3}$
Проверка:
$(-2 - \sqrt{3})^2 + 4(-2 - \sqrt{3}) + 1 = (2 + \sqrt{3})^2 - 8 - 4\sqrt{3} + 1 = 4 + 4\sqrt{3} + 3 - 8 - 4\sqrt{3} + 1 = 0$
$(-2 + \sqrt{3})^2 + 4(-2 + \sqrt{3}) + 1 = 4 - 4\sqrt{3} + 3 - 8 + 4\sqrt{3} + 1 = 0$

$3y^2 - 4y - 2 = 0$
$D = 2^2 + 3 * 2 = 4 + 6 = 10$
$y_{1,2} = \frac{2 ± \sqrt{10}}{3}$
Проверка:
$3(\frac{2 - \sqrt{10}}{3})^2 - 4(\frac{2 - \sqrt{10}}{3}) - 2 = \frac{3}{9}(4 - 4\sqrt{10} + 10) - \frac{8}{3} + \frac{4\sqrt{10}}{3} - 2 = \frac{4}{3} - \frac{4\sqrt{10}}{3} + \frac{10}{3} - \frac{8}{3} + \frac{4\sqrt{10}}{3} - 2 = 0$
$3(\frac{2 + \sqrt{10}}{3})^2 - 4(\frac{2 + \sqrt{10}}{3}) - 2 = \frac{3}{9}(4 + 4\sqrt{10} + 10) - \frac{8}{3} - \frac{4\sqrt{10}}{3} - 2 = \frac{4}{3} + \frac{4\sqrt{10}}{3} + \frac{10}{3} - \frac{8}{3} - \frac{4\sqrt{10}}{3} - 2 = 0$

$5y^2 - 7y + 1 = 0$
$D = 7^2 - 4 * 5 = 49 - 20 = 29$
$y_{1,2} = \frac{7 ± \sqrt{29}}{10}$
Проверка:
$5(\frac{7 - \sqrt{29}}{10})^2 - 7(\frac{7 - \sqrt{29}}{10}) + 1 = \frac{5}{100}(49 - 14\sqrt{29} + 29) - \frac{49}{10} + \frac{7\sqrt{29}}{10} + 1 = \frac{49}{20} - \frac{7\sqrt{29}}{10} + \frac{29}{20} - \frac{98}{20} + \frac{7\sqrt{29}}{10} + \frac{20}{20} = 0$
$5(\frac{7 + \sqrt{29}}{10})^2 - 7(\frac{7 + \sqrt{29}}{10}) + 1 = \frac{5}{100}(49 + 14\sqrt{29} + 29) - \frac{49}{10} - \frac{7\sqrt{29}}{10} + 1 = \frac{49}{20} + \frac{7\sqrt{29}}{10} + \frac{29}{20} - \frac{98}{20} - \frac{7\sqrt{29}}{10} + \frac{20}{20} = 0$

$2y^2 + 11y + 10 = 0$
$D = 11^2 - 4 * 2 * 10 = 121 - 80 = 41$
$y_{1,2} = \frac{-11 ± \sqrt{41}}{4}$
Проверка:
$2(\frac{-11 - \sqrt{41}}{4})^2 + 11(\frac{-11 - \sqrt{41}}{4}) + 10 = \frac{2}{16}(121 + 22\sqrt{41} + 41) - \frac{121}{4} - \frac{11\sqrt{41}}{4} + 10 = \frac{121}{8} + \frac{11\sqrt{41}}{4} + \frac{41}{8} - \frac{242}{8} - \frac{11\sqrt{41}}{4} + \frac{80}{8} = 0$
$2(\frac{-11 + \sqrt{41}}{4})^2 + 11(\frac{-11 + \sqrt{41}}{4}) + 10 = \frac{2}{16}(121 - 22\sqrt{41} + 41) - \frac{121}{4} + \frac{11\sqrt{41}}{4} + 10 = \frac{121}{8} - \frac{11\sqrt{41}}{4} + \frac{41}{8} - \frac{242}{8} + \frac{11\sqrt{41}}{4} + \frac{80}{8} = 0$

$4x^2 - 9x - 2 = 0$
$D = 9^2 + 4 * 4 * 2 = 81 + 32 = 113$
$x_{1,2} = \frac{9 ± \sqrt{113}}{8}$
Проверка:
$4(\frac{9 - \sqrt{113}}{8})^2 - 9(\frac{9 - \sqrt{113}}{8}) - 2 = \frac{4}{64}(81 - 18\sqrt{113} + 113) - \frac{81}{8} + \frac{9\sqrt{113}}{8} - 2 = \frac{81}{16} - \frac{9\sqrt{113}}{8} + \frac{113}{16} - \frac{162}{16} + \frac{9\sqrt{113}}{8} - \frac{32}{16} = 0$
$4(\frac{9 + \sqrt{113}}{8})^2 - 9(\frac{9 + \sqrt{113}}{8}) - 2 = \frac{4}{64}(81 + 18\sqrt{113} + 113) - \frac{81}{8} - \frac{9\sqrt{113}}{8} - 2 = \frac{81}{16} + \frac{9\sqrt{113}}{8} + \frac{113}{16} - \frac{162}{16} - \frac{9\sqrt{113}}{8} - \frac{32}{16} = 0$