To solve this equation, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

First, let's simplify the expression inside the parentheses:

20 * (1 + 1/3x) - 17.8 = 1/5

20 * (4/3x) - 17.8 = 1/5

80/3x - 17.8 = 1/5

Now, let's get rid of the fractions by multiplying both sides of the equation by 15:

15 (80/3x - 17.8) = 15 1/5

15 80/3x - 15 17.8 = 3

400x - 267 = 3

Next, add 267 to both sides to isolate x:

400x = 270

Now, divide by 400 to solve for x:

x = 270/400

x = 0.675

Therefore, the solution to the equation is x = 0.675.