Решите разумные уравнения(все не считая 2.84, 2.85)

2.86. 
x - 2x - 18x - 6x + 9 = 0
Лицезреем, что x = -1 является корнем уравнения:
1 + 2 - 18 + 6 + 9 = 0
x + x - 3x - 3x - 15x - 15x + 9x + 9 = 0
x(x + 1) - 3x(x + 1) - 15x(x + 1) + 9(x + 1) = 0
(x - 3x - 15x + 9)(x + 1) = 0
x = -1
x - 3x - 15x + 9 = 0
x + 3x - 6x - 18x + 3x + 9 = 0
x(x + 3) - 6x(x + 3) + 3(x + 3) = 0
(x + 3)(x - 6x + 3) = 0
x = -3
x - 6x + 3 = 0
x - 6x + 9 - 6 = 0
(x - 3) - (6) = 0
(x - 3 - 6)(x - 3 + 6) = 0
x = 3 + 6; 3 - 6
Ответ: x = -3; -1; 3 - 6; 3 + 6.

2.87.
4x - 8x + 3x - 8x + 4 = 0 
Это возвратное уравнение. Разделяем на x.
4x - 8x + 3 - 8/x + 4/x = 0
4x + 4/x + 3 - 8x - 8/x = 0
4x + 8 + 4/x - 8x - 8/x - 5 = 0
4(x + 2 + 1/x) - 8(x + 1/x) - 5 = 0
4(x + 1/x) - 8(x + 1/x) - 5 = 0 
Пусть x + 1/x = t.
4t - 8t - 5 = 0
D = 64 + 544 = 164 + 165 = 169 = 12
t = (8 + 12)/8 = 20/8 = 5/2
t = (8 - 12)/8 = -4/8 = -1/2
Оборотная подмена:
1) x + 1/x = 5/2
2x + 2 = 5x
2x - 5x + 2 = 0
2x - 4x - x + 2 = 0
2x(x - 2) - (x - 2) = 0
(2x - 1)(x - 2) = 0
x = 1/2; 2.
2) x + 1/x = -1/2
2x + 2 = -x
2x + x + 2 = 0
D = 1 - 224 lt; 0  нет корней
Ответ: x = 1/2; 2. 

2.88
3x + 5x + 5/x + 3/x = 16
3x + 6 + 3/x + 5x + 5/x - 16 - 6 = 0
3(x + 2 + 1/x) + 5(x + 1/x) - 22 = 0
3(x + 1/x) + 5(x + 1/x) - 22 = 0
Пусть t = 1 + 1/x.
3t + 5t - 22 = 0
D = 25 + 2243 = 289 = 17
t = (-5 + 17)/6 = 12/6 = 2
t = (-5 - 17)/6 = -22/6 = -11/3
Оборотная подмена:
x + 1/x = 2
x + 1 = 2x
x - 2x + 1 = 0
(x - 1) = 0
x = 1
2) x + 1/x = -11/3
3x + 3 = -11x
3x + 11x + 3 = 0
D = 11 - 334 = 121 - 36 = 85 = (85)
x = (-11 + 85)/6
x = (-11 - 85)/6
Ответ: x = (-11 - 85)/6; (-11 + 85)/6; 1. 

2.89.
x - 2x - 13x - 2x + 1 = 0
Тоже возвратимое уравнение.
Разделим на x.
x - 2x - 13 - 2/x + 1/x = 0
x + 1/x - 2x - 2/x - 13 = 0
x + 2 + 1/x - 2x - 2/x - 13 - 2 = 0
(x + 1/x) - 2(x + 1/x) - 15 = 0
Пусть t = 1 + 1/x.
t - 2t - 15 = 0
t - 2t + 1 - 16 = 0
(t - 1) - 4 = 0
(t - 1 - 4)(t - 1 + 4) = 0
(t - 5)(t + 3) = 0
t = -3; 5
Оборотная замена:
1) x + 1/x = -3
x + 1 = -3x
x + 3x + 1 = 0
D = 9 - 4 = 5 = (5)
x = (-3 + 5)/2
x = (-3 - 5)/2
2) x + 1/x = 5
x + 1 = 5x
x - 5x + 1 = 0
D = 25 - 4 = 21 = (21)
x = (5 + 21)/2
x = (5 - 21)/2
Ответ: x = (-3 - 5)/2;  (-3 + 5)/2;  (5 - 21)/2;  (5 + 21)/2.