Choice A is the correct answer. You can solve this by factoring or using square roots.

Method 1 (Factoring):

1. Recognize difference of squares: $(2x)^2 - 3^2 = 0$.
2. Factor: $(2x - 3)(2x + 3) = 0$.
3. Solve: $2x = 3 \Rightarrow x = 3/2$ and $2x = -3 \Rightarrow x = -3/2$.

Method 2 (Square Roots):

1. Isolate $x^2$: $4x^2 = 9 \Rightarrow x^2 = 9/4$.
2. Take square root: $x = \pm \sqrt{9/4} = \pm 3/2$.

Choice B is incorrect because it forgets to take the square root. Choice C is incorrect because it misses the negative solution. Choice D is incorrect because the fraction is inverted (should be $\sqrt{9}/\sqrt{4}$).