2n^2-18n-4000=0

Solution for 2n^2-18n-4000=0 equation:

2n^2-18n-4000=0

a = 2; b = -18; c = -4000;
Δ = b2-4ac
Δ = -182-4·2·(-4000)
Δ = 32324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32324}=\sqrt{4*8081}=\sqrt{4}*\sqrt{8081}=2\sqrt{8081}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{8081}}{2*2}=\frac{18-2\sqrt{8081}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{8081}}{2*2}=\frac{18+2\sqrt{8081}}{4}
$