n2+2n=10,439361

Solution for n2+2n=10,439361 equation:

n2+2n=10.439361

We move all terms to the left:

n2+2n-(10.439361)=0

We add all the numbers together, and all the variables

n^2+2n-10.439361=0

a = 1; b = 2; c = -10.439361;
Δ = b2-4ac
Δ = 22-4·1·(-10.439361)
Δ = 45.757444
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{-(2)-\sqrt{45.757444}}{2*1}=\frac{-2-\sqrt{45.757444}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+\sqrt{45.757444}}{2*1}=\frac{-2+\sqrt{45.757444}}{2}
$