Решите уравнение (1-3x)(x+1)=(3x-1)(2x+1)

Question

Решите уравнение
(1-3x)(x+1)=(3x-1)(2x+1)

Answer 1

(1 - 3x)(x + 1) = (3x - 1)(2x + 1)
x + 1 - 3x² - 3x = 6x² + 3x - 2x - 1
-3x² - 2x + 1 = 6x² + x - 1
-9x² - 3x + 2 = 0
-9x² - 3x + 2 = 0
9x² + 3x - 2 = 0
D = 9 + 9·2·4 = 81 = 9²
x₁ = (-3 - 9)/18 = -12/18 = -2/3
x₂ = (-3 + 9)/18 = -6/18 = 1/3
Ответ: x = -2/3; 1/3.