10(x-2)^2 - 5x(2x-1) = 3x

10(x^2 - 4x + 4) - 5x(2x) + 5x = 3x

10x^2 - 40x + 40 - 10x^2 + 5x^2 + 5x = 3x

-40x + 40 + 5x^2 + 5x = 3x

5x^2 - 40x + 5x + 40 = 3x

5x^2 - 35x + 40 = 3x

5x^2 - 38x + 40 = 0

Теперь решим это уравнение с помощью метода завершения квадратов:

5(x^2 - 7.6x) + 40 = 0

5(x^2 - 7.6x + 11.36) - 5(11.36) + 40 = 0

5(x - 3.8)^2 - 56.8 + 40 = 0

5(x - 3.8)^2 - 16.8 = 0

5(x - 3.8)^2 = 16.8

(x - 3.8)^2 = 16.8 / 5

(x - 3.8)^2 = 3.36

x - 3.8 = ±√3.36

x - 3.8 = ±1.83

x = 3.8 ± 1.83

x₁ = 5.63
x₂ = 1.97

Ответ: x₁ = 5.63, x₂ = 1.97