110q=-q^2+6000

Solution for 110q=-q^2+6000 equation:

110q=-q^2+6000

We move all terms to the left:

110q-(-q^2+6000)=0

We get rid of parentheses

q^2+110q-6000=0

a = 1; b = 110; c = -6000;
Δ = b2-4ac
Δ = 1102-4·1·(-6000)
Δ = 36100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36100}=190$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-190}{2*1}=\frac{-300}{2}
=-150
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+190}{2*1}=\frac{80}{2}
=40
$