$x^2 + bx + c = 0$
$x_1 = -7$
$x_2 = -8$
$x_1 + x_2 = -b$
−7 + (−8) = −b
−15 = −b
b = 15
$x_1x_2 = с$
−7 * (−8) = c
c = 56
$x^2 + 15x + 56 = 0$
Ответ: $x^2 + 15x + 56 = 0$

$x^2 + bx + c = 0$
$x_1 = 5$
$x_2 = -0,4$
$x_1 + x_2 = -b$
5 + (−0,4) = −b
4,6 = −b
b = −4,6
$x_1x_2 = с$
5 * (−0,4) = c
c = −2
$x^2 - 4,6x - 2 = 0$ |* 10
$10x^2 - 46x - 20 = 0$
Ответ: $10x^2 - 46x - 20 = 0$

$x^2 + bx + c = 0$
$x_1 = \frac{1}{2}$
$x_2 = \frac{2}{3}$
$x_1 + x_2 = -b$
$\frac{1}{2} + \frac{2}{3} = -b$
$\frac{3}{6} + \frac{4}{6} = -b$
$\frac{7}{6} = -b$
$b = -\frac{7}{6}$
$x_1x_2 = с$
$\frac{1}{2} * \frac{2}{3} = c$
$c = \frac{1}{3}$
$x^2 - \frac{7}{6}x + \frac{1}{3} = 0$ |* 6
$6x^2 - 7x + 2 = 0$
Ответ: $6x^2 - 7x + 2 = 0$

$x^2 + bx + c = 0$
$x_1 = 5 - \sqrt{10}$
$x_2 = 5 + \sqrt{10}$
$x_1 + x_2 = -b$
$5 - \sqrt{10} + 5 + \sqrt{10} = -b$
10 = −b
b = −10
$x_1x_2 = с$
$(5 - \sqrt{10})(5 + \sqrt{10}) = c$
$c = 5^2 - (\sqrt{10})^2$
c = 25 − 10
c = 15
$x^2 - 10x + 15 = 0$
Ответ: $x^2 - 10x + 15 = 0$