20000=-19n+7n^2

Solution for 20000=-19n+7n^2 equation:

20000=-19n+7n^2

We move all terms to the left:

20000-(-19n+7n^2)=0

We get rid of parentheses

-7n^2+19n+20000=0

a = -7; b = 19; c = +20000;
Δ = b2-4ac
Δ = 192-4·(-7)·20000
Δ = 560361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{560361}}{2*-7}=\frac{-19-\sqrt{560361}}{-14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{560361}}{2*-7}=\frac{-19+\sqrt{560361}}{-14}
$