(2z² + 11z)² - 23(2z² + 11z) + 126 = 0
Пусть 2z² + 11z = t, тогда
t² - 23t + 126 = 0
D = 529 - 504 = 25
t₁ = (23 + 5)/2 = 14
t₂ = (23 - 5)/2 = 9
Обратная замена, 2 случая
1) 2z² + 11z = 9
2z² + 11z - 9 = 0
D = 193
x₁ = ( - 11 + √193)/4;
x₂ = ( - 11 - √193)/4;
2) 2z² + 11z = 14
2z² + 11x - 14 = 0
D = 233
x₃ = ( - 11 + √233)/4;
x₄ = ( - 11 - √233)/4;
Ответ
( - 11 + √193)/4
( - 11 - √193)/4
( - 11 + √233)/4
( - 11 - √233)/4