n^2+5n+18=73630940=n=10000

Solution for n^2+5n+18=73630940=n=10000 equation:

n^2+5n+18=73630940=n=10000

We move all terms to the left:

n^2+5n+18-(73630940)=0

We add all the numbers together, and all the variables

n^2+5n-73630922=0

a = 1; b = 5; c = -73630922;
Δ = b2-4ac
Δ = 52-4·1·(-73630922)
Δ = 294523713
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:

$\sqrt{\Delta}=\sqrt{294523713}=\sqrt{9*32724857}=\sqrt{9}*\sqrt{32724857}=3\sqrt{32724857}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{32724857}}{2*1}=\frac{-5-3\sqrt{32724857}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{32724857}}{2*1}=\frac{-5+3\sqrt{32724857}}{2}
$