n^2+n=10^5

Solution for n^2+n=10^5 equation:

n^2+n=10^5

We move all terms to the left:

n^2+n-(10^5)=0

We add all the numbers together, and all the variables

n^2+n-100000=0

a = 1; b = 1; c = -100000;
Δ = b2-4ac
Δ = 12-4·1·(-100000)
Δ = 400001
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{-(1)-\sqrt{400001}}{2*1}=\frac{-1-\sqrt{400001}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{400001}}{2*1}=\frac{-1+\sqrt{400001}}{2}
$