Choice A is the correct answer.

1. Identify: $a=1, b=-6, c=7$.
2. Discriminant: $(-6)^2 - 4(1)(7) = 36 - 28 = 8$.
3. Formula: $x = \frac{-(-6) \pm \sqrt{8}}{2(1)} = \frac{6 \pm 2\sqrt{2}}{2}$.
4. Simplify: Divide both terms by 2: $3 \pm \sqrt{2}$.

Choice B is incorrect because it forgets to divide the 6 by 2. Choice C is incorrect because it simplifies $\sqrt{8}$ as 2 (it is approx 2.82). Choice D is incorrect because it uses $-6$ instead of $-(-6)$.