Let's solve the given equation step by step:

0.4(x-5) - 0.8(x-2) = 3.4

First, distribute the constants inside the parentheses:

0.4x - 2 - 0.8x + 1.6 = 3.4

Combine like terms:

-0.4x - 0.4 = 3.4

Add 0.4 to both sides:

-0.4x = 3.8

Divide by -0.4 to solve for x:

x = -9.5

Therefore, the solution to the equation is x = -9.5.