1)x² - 4(x - 2) + 3x -14 = 0
x² - 4x + 8 + 3x - 14 = 0
x² - x -6 = 0
D = (-1)² - 4 * 1 * (-6) = 1 + 24 = 25
√D = √25 = 5
x = (1 ± 5) / 2 * 1
x1 = (1 + 5) / 2 = 3
x2 = (1 - 5) / 2 = -2
Ответ: x1 = 3; x2 = -2
2)4x² - 3(x² - 2x) - 10 = 6
4x² - 3x² + 6x = 6 + 10
x² + 6x - 16 = 0
D = 6² - 4 * 1 * (-16) = 36 + 64 = 100
√D = √100 = 10
x = (-6 ± 10) / 2 * 1
x1 = (-6 + 10) / 2 = 2
x2 = (-6 - 10) / 2 = -8
Ответ: x1 = 2; x2 = -8
3)5x² - 3(x² + 2x) + 3x + 9 = 14
5x² - 3x² - 6x + 3x = 14 - 9
2x² - 3x - 5 = 0
D = (-3)² - 4 * 2 * (-5) = 9 +40 = 49
√D = √49 = 7
x = (3 ± 7) / 2 * 2
x1 = (3 + 7) / 4 = 2,5
x2 = (3 - 7) / 4 = -1
Ответ: x1 = 2,5; x2 = -1
4)(2x + 3)(3x + 1) - 10 = 11x + 20
6x² + 2x + 9x +3 - 10 - 11x - 20 = 0
6x² + 11x - 27 - 11x = 0
6x² = 27
x² = 4,5
x = ±√4,5
Ответ: х1 = ±√4,5