n2+2n=19,175641

Solution for n2+2n=19,175641 equation:

n2+2n=19.175641

We move all terms to the left:

n2+2n-(19.175641)=0

We add all the numbers together, and all the variables

n^2+2n-19.175641=0

a = 1; b = 2; c = -19.175641;
Δ = b2-4ac
Δ = 22-4·1·(-19.175641)
Δ = 80.702564
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{80.702564}}{2*1}=\frac{-2-\sqrt{80.702564}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+\sqrt{80.702564}}{2*1}=\frac{-2+\sqrt{80.702564}}{2}
$