Let's first expand both sides of the equation:

(1/2 - 5x)^2 + 3/4 = (5x - 4)^2

Expanding the left side:

(1/2 - 5x)^2 = (1/2 - 5x)(1/2 - 5x)
= 1/4 - 5x/2 - 5x/2 + 25x^2
= 1/4 - 5x + 25x^2

Therefore, the left side of the equation becomes:

(1/4 - 5x + 25x^2) + 3/4
= 1/4 - 5x + 25x^2 + 3/4
= 25x^2 - 5x + 1

Expanding the right side:

(5x - 4)^2 = (5x - 4)(5x - 4)
= 25x^2 - 20x - 20x + 16
= 25x^2 - 40x + 16

Now, our equation becomes:

25x^2 - 5x + 1 = 25x^2 - 40x + 16

Now we can simplify the equation by subtracting 25x^2 from both sides:

-5x + 1 = -40x + 16

Rearrange the terms to get:

40x - 5x = 16 - 1
35x = 15
x = 15/35
x = 3/7

Therefore, the solution to the equation is x = 3/7.