Let's solve the given equation step by step:

(7 + 0.004x)/0.9 / 24.7 - 12.3 = 77.7

First, simplify the expression within the parentheses:
(7 + 0.004x) / 0.9 = (7/0.9 + 0.004x/0.9) = (7.7778 + 0.0044x)

Now, rewrite the equation with the simplified expression:
(7.7778 + 0.0044x) / 24.7 - 12.3 = 77.7

Next, multiply the numerator by 1 so that the fraction remains the same:
(7.7778 + 0.0044x) / 24.7 - 12.3 = 77.7
[(7.7778 + 0.0044x) / 24.7] * 1 - 12.3 = 77.7

Now, simplify the expression within the brackets:
(7.7778 + 0.0044x) / 24.7 = (7.7778 / 24.7 + 0.0044x / 24.7) = (0.3152 + 0.000179x)

Rewrite the equation with the simplified expression:
(0.3152 + 0.000179x) - 12.3 = 77.7

Now, combine like terms:
0.3152 + 0.000179x - 12.3 = 77.7
0.000179x - 11.9848 = 77.7

Add 11.9848 to both sides:
0.000179x = 89.6848

Now, divide by 0.000179 to solve for x:
x = 501000

Therefore, the solution to the equation is x = 501000.