(2x-1)^2 +5(2x-1)+6=0

(2x - 1)² + 5(2x - 1) + 6 = 0

Сделаем замену :

2x - 1 = m

m² + 5m + 6 = 0

D = 5² - 4 * 6 = 25 - 24 = 1

1) 2x - 1 = - 3

2x = - 2

x₁ = - 1

2) 2x - 1 = - 2

2x = - 1

x₂ = - 0,5

Ответ : - 0,5 ; - 1

(2x-1)²+5(2x-1)+6=0

4х² - 4х + 1 + 10х - 5 + 6 = 0

4х²+6х+2 = 0

2х²+3х + 1 = 0

(2х+1)(х+1) = 0

х₁ = -0,5

х₂ = -1