n^2-5n-1000=0

Solution for n^2-5n-1000=0 equation:

n^2-5n-1000=0

a = 1; b = -5; c = -1000;
Δ = b2-4ac
Δ = -52-4·1·(-1000)
Δ = 4025
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:

$\sqrt{\Delta}=\sqrt{4025}=\sqrt{25*161}=\sqrt{25}*\sqrt{161}=5\sqrt{161}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{161}}{2*1}=\frac{5-5\sqrt{161}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{161}}{2*1}=\frac{5+5\sqrt{161}}{2}
$