where from this solving this quadratic equation gives q = 30 ± sqrt(100) = 30 ± 10.

The given statement seems to be the solution of a quadratic equation. Here's how it might have been derived:

1. A quadratic equation is generally in the form ax^2 + bx + c = 0. The solutions of this equation can be found using the quadratic formula: x = [-b ± sqrt(b^2 - 4ac)] / (2a).

2. In the given statement, it seems that the solutions are q = 30 ± 10. This suggests that the equation was in the form of q = [-b ± sqrt(b^2 - 4ac)] / (2a).

3. To get q = 30 ± 10, the value inside the square root (the discriminant, b^2 - 4ac) must be 100, because sqrt(100) = 10.

4. Also, the value of -b/2a must be 30, because that's the number being added to and subtracted from in the solutions.

5. Without the original equation, it's impossible to know the exact values of a, b, and c. But the solutions suggest that the equation was manipulated into the form q = [-b ± sqrt(b^2 - 4ac)] / (2a) and then solved, giving q = 30 ± 10.