Let's expand and simplify the equation step by step:

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

First, expand both sides:

(1/2 - 5x)^2 = (1/2 - 5x)(1/2 - 5x) = 1/4 - 5/2x - 5/2x + 25x^2 = 1/4 - 5x - 5x + 25x^2 = 1/4 - 10x + 25x^2

And simplify:

(1/2 - 5x)^2 = 1/4 - 10x + 25x^2

Now, substitute back into the original equation:

1/4 - 10x + 25x^2 + 3/4 = (5x - 4)^2
1 - 10x + 25x^2 + 3 = (5x - 4)^2
4 - 10x + 25x^2 = (5x - 4)^2

Now let's expand the right side of the equation:

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

Now, substitute back into the equation:

4 - 10x + 25x^2 = 25x^2 - 40x + 16

Now we will simplify this equation further by arranging the terms:

4 - 10x = -40x + 16
4 = -30x + 16
-12 = -30x
x = 12/30
x = 2/5

Therefore, the solution to the given equation is x = 2/5.