To solve the given equation, we can rewrite it as:

sqrt(3)*sin(x)/4 - cos(x)/4 = 0

Now, we can rewrite it as:

sqrt(3)*sin(x) = cos(x)

Now, we can square both sides to eliminate the square root:

3*sin^2(x) = cos^2(x)

Using the trigonometric identity cos^2(x) + sin^2(x) = 1, we get:

3 - 3*cos^2(x) = cos^2(x)

Expanding the equation:

3 = 4*cos^2(x)

Dividing both sides by 4:

3/4 = cos^2(x)

Taking the square root of both sides:

cos(x) = ±sqrt(3)/2

Therefore, the solutions for x are:

x = π/6 + 2nπ, 5π/6 + 2nπ, where n is an integer.