Answer: The first interval:0 ≤ x ≤ 20
Procedure
You have to solve this inequality
-2x^2 +40x +600 ≥ 600
-2x^2 +40x ≥ 0
-x^2+20x ≥ 0
x^2 - 20 x ≤ 0
x(x-20) ≤ 0
That is only possible if the two factors have different signs.
Let's examine the possibilities
x ≥ 0 and x -20 ≤ 0⇔x≤20, that is 0≤x≤20
The other possibility is
x ≤ 0 and x - 20 ≥ 0 ⇔x≥20. This conditions is not possible.
So the solution is 0≤x≤20
