I understand the quadratic formula. I can derive the quadratic formula. I do not understand what to do when b= the sum of two square roots, as in the following problem:

Use the quadratic formula to solve:

r squared + [square root (3) - square root (2)]*r = square root (6)

r^2+(√(3)-√(2))r = √(6)

I know the answer is r = -(√(3)) or √(2). I don't know how to get to that answer. I have tried a number of ways. Plugging a, b, and c straight into the quadratic formula, I get:

r = 1/2[√(2)-√(3)+√(5+(2√(6)))] or 1/2[√(2)-√(3)-√(5+(2√(6)))]

This is right, but I don't understand the following steps:

1/2[√(2)-√(3)+√(5+(2√(6)))] --> √(2)

1/2[√(2)-√(3)-√(5+(2√(6)))] --> -(√(3))

Thanks for your help! (I've been working on this problem for WAY too long.)