To solve the equation, we can start by expanding the left side of the equation:

(3/4 - 7x)^2 = 1/4

(3/4 - 7x)(3/4 - 7x) = 1/4

(9/16 - 21/4x + 49x^2) = 1/4

Now, let's simplify the equation:

9/16 - 21/4x + 49x^2 = 1/4

To eliminate the fractions, we can multiply both sides of the equation by 16:

16(9/16 - 21/4x + 49x^2) = 16(1/4)

9 - 84x + 784x^2 = 4

Rearranging the equation:

784x^2 - 84x + 5 = 0

Now, we can solve this quadratic equation by factoring or using the quadratic formula. However, this equation does not factor easily, so we will use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 784, b = -84, and c = 5. Plugging these values into the quadratic formula:

x = (-(-84) ± √((-84)^2 - 4(784)(5))) / (2(784))

x = (84 ± √(7056 - 15680)) / 1568

x = (84 ± √(-8624)) / 1568

Since the discriminant (b^2 - 4ac) is negative, the equation has no real solutions.