To solve this equation, let's make a substitution to simplify it:

Let y = cos^2(x).

Now we can rewrite the equation as:

16y^2 - 24y + 9 = 0

This is now a quadratic equation that we can solve using the quadratic formula:

y = [ -(-24) ± √((-24)^2 - 4169) ] / 2*16
y = [ 24 ± √(576 - 576) ] / 32
y = [ 24 ± 0 ] / 32
y = 24 / 32
y = 3/4

Now substitute back in cos^2(x) for y:

cos^2(x) = 3/4

Taking the square root of both sides, we get:

cos(x) = ±√(3/4)
cos(x) = ±√3 / 2

Therefore, the solutions are:

x = ±π/6 and x = ±5π/6.