-5n^2+21n+4000=0

Solution for -5n^2+21n+4000=0 equation:

-5n^2+21n+4000=0

a = -5; b = 21; c = +4000;
Δ = b2-4ac
Δ = 212-4·(-5)·4000
Δ = 80441
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{-(21)-\sqrt{80441}}{2*-5}=\frac{-21-\sqrt{80441}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{80441}}{2*-5}=\frac{-21+\sqrt{80441}}{-10}
$