n2-2n-3=5000

Solution for n2-2n-3=5000 equation:

n2-2n-3=5000

We move all terms to the left:

n2-2n-3-(5000)=0

We add all the numbers together, and all the variables

n^2-2n-5003=0

a = 1; b = -2; c = -5003;
Δ = b2-4ac
Δ = -22-4·1·(-5003)
Δ = 20016
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:

$\sqrt{\Delta}=\sqrt{20016}=\sqrt{144*139}=\sqrt{144}*\sqrt{139}=12\sqrt{139}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-12\sqrt{139}}{2*1}=\frac{2-12\sqrt{139}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+12\sqrt{139}}{2*1}=\frac{2+12\sqrt{139}}{2}
$