n^2+15n-2000=0

Solution for n^2+15n-2000=0 equation:

n^2+15n-2000=0

a = 1; b = 15; c = -2000;
Δ = b2-4ac
Δ = 152-4·1·(-2000)
Δ = 8225
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:

$\sqrt{\Delta}=\sqrt{8225}=\sqrt{25*329}=\sqrt{25}*\sqrt{329}=5\sqrt{329}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{329}}{2*1}=\frac{-15-5\sqrt{329}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{329}}{2*1}=\frac{-15+5\sqrt{329}}{2}
$