(3-2x)(6x-1) = (2x-3)^218x - 3 - 12x^2 + 2x = 4x^2 - 12x + 918x - 3 - 12x^2 + 2x = 4x^2 - 12x + 9-12x^2 + 18x + 2x - 3 = 4x^2 - 12x + 9-12x^2 + 20x - 3 = 4x^2 - 12x + 9-12x^2 - 4x^2 + 20x + 12x - 3 - 9 = 0-16x^2 + 32x - 12 = 04x^2 - 8x + 3 = 0
Теперь решим квадратное уравнение
D = b^2 - 4acD = (-8)^2 - 443D = 64 - 48D = 16
x1 = (-b + √D) / 2ax1 = (8 + √16) / (2*4)x1 = 12 / 8x1 = 1.5
x2 = (-b - √D) / 2ax2 = (8 - √16) / (2*4)x2 = 4 / 8x2 = 0.5
Ответ: x1 = 1.5, x2 = 0.5.
(3-2x)(6x-1) = (2x-3)^2
18x - 3 - 12x^2 + 2x = 4x^2 - 12x + 9
18x - 3 - 12x^2 + 2x = 4x^2 - 12x + 9
-12x^2 + 18x + 2x - 3 = 4x^2 - 12x + 9
-12x^2 + 20x - 3 = 4x^2 - 12x + 9
-12x^2 - 4x^2 + 20x + 12x - 3 - 9 = 0
-16x^2 + 32x - 12 = 0
4x^2 - 8x + 3 = 0
Теперь решим квадратное уравнение
D = b^2 - 4ac
D = (-8)^2 - 443
D = 64 - 48
D = 16
x1 = (-b + √D) / 2a
x1 = (8 + √16) / (2*4)
x1 = 12 / 8
x1 = 1.5
x2 = (-b - √D) / 2a
x2 = (8 - √16) / (2*4)
x2 = 4 / 8
x2 = 0.5
Ответ: x1 = 1.5, x2 = 0.5.