n^2+13n+42=100000

Solution for n^2+13n+42=100000 equation:

n^2+13n+42=100000

We move all terms to the left:

n^2+13n+42-(100000)=0

We add all the numbers together, and all the variables

n^2+13n-99958=0

a = 1; b = 13; c = -99958;
Δ = b2-4ac
Δ = 132-4·1·(-99958)
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{-(13)-\sqrt{400001}}{2*1}=\frac{-13-\sqrt{400001}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{400001}}{2*1}=\frac{-13+\sqrt{400001}}{2}
$