Choice A is the correct answer. First, rewrite in standard form: $x^2 + 4x - 1 = 0$.

1. Identify: $a=1, b=4, c=-1$.
2. Discriminant: $4^2 - 4(1)(-1) = 16 + 4 = 20$.
3. Formula: $x = \frac{-4 \pm \sqrt{20}}{2}$.
4. Simplify: $\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}$.
5. $x = \frac{-4 \pm 2\sqrt{5}}{2} = -2 \pm \sqrt{5}$.

Choice B is incorrect because of a sign error on the linear term. Choice C is incorrect because it simplifies $\sqrt{20}$ incorrectly. Choice D is incorrect because it forgets to divide by 2.