-0.5q^2-199.8q+2400=0

Solution for -0.5q^2-199.8q+2400=0 equation:

-0.5q^2-199.8q+2400=0

a = -0.5; b = -199.8; c = +2400;
Δ = b2-4ac
Δ = -199.82-4·(-0.5)·2400
Δ = 44720.04
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-199.8)-\sqrt{44720.04}}{2*-0.5}=\frac{199.8-\sqrt{44720.04}}{-1}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-199.8)+\sqrt{44720.04}}{2*-0.5}=\frac{199.8+\sqrt{44720.04}}{-1}
$