Explain why a positive discriminant results in two real solutions ...

You have three cases for a discriminant:

1. Zero

A zero in the discriminant means that there is one solution, since it's ... plus/minus zero, which is just ...

2. Negative

Negative means no real solutions, as the square root of a negative number is not real.

3. Positive

If you have a positive number within the square root, it means that your solutions will be ... plus/minus whatever the square root is. One solution is the plus, and one solution is the minus, hence two solutions.