55000=-2.6q^2+900q

Solution for 55000=-2.6q^2+900q equation:

55000=-2.6q^2+900q

We move all terms to the left:

55000-(-2.6q^2+900q)=0

We get rid of parentheses

2.6q^2-900q+55000=0

a = 2.6; b = -900; c = +55000;
Δ = b2-4ac
Δ = -9002-4·2.6·55000
Δ = 238000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{238000}=\sqrt{400*595}=\sqrt{400}*\sqrt{595}=20\sqrt{595}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-20\sqrt{595}}{2*2.6}=\frac{900-20\sqrt{595}}{5.2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+20\sqrt{595}}{2*2.6}=\frac{900+20\sqrt{595}}{5.2}
$