$y = \frac{5x - 7}{x^2 + 1}$
$y(x^2 + 1) = 5x - 7$
$yx^2 - 5x + (y + 7) = 0$
 
при y = −6:
$-6x^2 - 5x + (-6 + 7) = 0$
$-6x^2 - 5x + 1 = 0$
$6x^2 + 5x - 1 = 0$
D = 25 + 4 * 6 = 25 + 24 = 49
$x = \frac{-5 ± \sqrt{49}}{6}$
$x_1 = \frac{-5 - 7}{6} = \frac{-12}{6} = -2$
$x_2 = \frac{-5 + 7}{6} = \frac{2}{6} = \frac{1}{3}$
Ответ: при y = 6:
$x_1 = -2$;
$x_2 = \frac{1}{3}$.
 
при y = 0:
0 − 5x + (0 + 7) = 0
−5x + 7 = 0
−5x = −7
x = 1,4
Ответ: при y = 0:
x = 1,4
 
при y = 0,8:
$0,8x^2 - 5x + (0,8 + 7) = 0$
$0,8x^2 - 5x + 7,8 = 0$
D = 25 − 4 * 0,8 * 7,8 = 25 − 24,96 = 0,04
$x = \frac{5 ± \sqrt{0,04}}{1,6}$
$x_1 = \frac{5 - 0,2}{1,6} = \frac{4,8}{1,6} = 3$
$x_2 = \frac{5 + 0,2}{1,6} = \frac{5,2}{1,6} = 3,25$
Ответ: при y = 0,8:
$x_1 = 3$;
$x_2 = 3,25$.
 
при y = 0,56:
$0,56x^2 - 5x + (0,56 + 7) = 0$
$0,56x^2 - 5x + 7,56 = 0$
D = 25 − 4 * 0,56 * 7,56 = 25 − 16,9344 = 8,0656
$x = \frac{5 ± \sqrt{8,0656}}{1,12}$
$x_1 = \frac{5 - 2,84}{1,12} = \frac{2,16}{1,12} = \frac{27}{14} = 1\frac{13}{14}$
$x_2 = \frac{5 + 2,84}{1,12} = \frac{7,84}{1,12} = 7$
Ответ: при y = 0,56:
$x_1 = 1\frac{13}{14}$;
$x_2 = 7$.

$y = \frac{x^2 - 2x + 6}{x + 4}$
$y(x + 4) = x^2 - 2x + 6$
$x^2 - (2 + y)x + 6 - 4y = 0$
 
при y = 1,5:
$x^2 - (2 + 1,5)x + 6 - 4 * 1,5 = 0$
$x^2 - 3,5x + 6 - 6 = 0$
$x^2 - 3,5x = 0$
x(x − 3,5) = 0
x = 0
или
x − 3,5 = 0
x = 3,5
Ответ: при y = 1,5:
$x_1 = 0$;
$x_2 = 3,5$.
 
при y = 3:
$x^2 - (2 + 3)x + 6 - 4 * 3 = 0$
$x^2 - 5x + 6 - 12 = 0$
$x^2 - 5x - 6 = 0$
D = 25 + 24 = 49
$x = \frac{5 ± \sqrt{49}}{2}$
$x_1 = \frac{5 - 7}{2} = \frac{-2}{2} = -1$
$x_2 = \frac{5 + 7}{2} = \frac{12}{2} = 6$
Ответ: при y = 1,5:
$x_1 = -1$;
$x_2 = 6$.
 
при y = 7:
$x^2 - (2 + 7)x + 6 - 4 * 7 = 0$
$x^2 - 9x + 6 - 28 = 0$
$x^2 - 9x - 22 = 0$
D = 81 + 4 * 22 = 81 + 88 = 169
$x = \frac{9 ± \sqrt{169}}{2}$
$x_1 = \frac{9 - 13}{2} = \frac{-4}{2} = -2$
$x_2 = \frac{9 + 13}{2} = \frac{22}{2} = 11$
Ответ: при y = 7:
$x_1 = -2$;
$x_2 = 11$.