1-1/2-x=6-x/3x-12-1/x-2

умножим знаменатель дроби в левой доли на (-1):
1 1 /  (- 1)(х 2) = (6 x) / (3x - 12) 1 / (x - 2);
1 + 1 / (x - 2) = (6 x) / 3(x - 4) 1 / (x - 2);
1 / (x - 2) - (6 x) / 3(x - 4) + 1 / (x - 2) = - 1;
2 / (x - 2) - (6 x) / 3(x - 2²) = - 1;
2  / (x - 2) - (6 x) / 3(x - 2)(х + 2) = - 1;
2 * 3(х + 2) / 3(x - 2)(х + 2) - (6 x) / 3(x - 2)(х + 2) = -1;

6(х + 2) / 3(x - 2)(х + 2) - (6 x) / 3(x - 2)(х + 2) = -1;
[6(х + 2) - (6 x)] / 3(x - 2)(х + 2) = -1;
(7 х + 6) / 3(x - 2)(х + 2) = -1
(7 х + 6) / 3(x² 2²) = -1
7 х + 6 = - 3 x² + 12;
7 х + 6 + 3 x² 12 = 0;
3 x² + 7 х  - 6 = 0;
Квадратное уравнение:
D = b² - 4 ac = 7² 4 * 3 *(- 6) = 49 + 72 = 121;
https://bit.ly/2Ub1TdM
Ответ : х₁ = - 1/3; х₂ = 3/2.