Решите уравнения:

1) (7 х-5) х = (1,5-2.1 х)

2) (1-8 х) х = (11,2 х-1,4)

3) (1,7 х-1/3) х = (3-15,3 х) * 1/2

4) (х/7-1 6/7) х = (3,9-0,3 х) * 1/35

1) (7 х-5) х = (1,5-2.1 х); 7 х²-5 х = 1,5 - 2.1 х| · 10; 70 х² - 50 х = 15 - 21 х; 70 х² - 29 х - 15 = 0;

D = 29² + 4·70·15 = 841 + 4200 = 5041; √D = 71; x₁ = (29 + 71) / 140 = 100/140=5/7;

x₂ = (29 - 71) / 140 = 42/140=3/20 = 0.15. Ответ: 5/7; 0,15.

2) (1 - 8 х) х = (11,2 х - 1,4); x - 8 х² = 11,2 х - 1,4|·5; 5x - 40 х² = 56 х - 7; 40 х² + 51x - 7 = 0; D = 51² + 1120 = 2601 + 1120 = 3721; √D = 61; x₁ = (-51 + 61) / 80 = 10/80 = 1/8 = 0,125; x₂ = (-51 - 61) / 80 = - 111/80 = - 1,3785. Ответ: 0,125; - 1,3785.

3) (1,7 х - 1/3) х = (3 - 15,3 х) * 1/2; 1,7 х² - (1/3) х = (3 - 15,3 х) * 1/2|·60; 102 х² - 20 х = (30 - 153 х) * 3; 102 х² - 20 х = 90 - 459 х; 102 х² + 439 х - 90 = 0; D = 439² + 360·102 = 229441; √D = 479; x₁ = (-439 + 479) / 204 = 40/204 = 10/51; x₂ = (-439 - 479) / 204 = - 918/204 = - 459/102 = - 153/34 = - 9/2 = - 4,5. Ответ: 10/51; - 4,5.

4) (х/7 - 1 (6/7)) х = (3,9-0,3 х) * 1/35|·350; 50x² - 650x = 39 - 3x; 50x² - 647x - 39 = 0; D = 418609 + 200·39 = 426409; √D = 653; x₁ = (650 + 653) / 100 = 13,03; x₂ = (650 - 653) / 100 = - 0,03. Ответ: 13,03; - 0,03.