n^2+2n+3=443

Solution for n^2+2n+3=443 equation:

n^2+2n+3=443

We move all terms to the left:

n^2+2n+3-(443)=0

We add all the numbers together, and all the variables

n^2+2n-440=0

a = 1; b = 2; c = -440;
Δ = b2-4ac
Δ = 22-4·1·(-440)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-42}{2*1}=\frac{-44}{2}
=-22
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+42}{2*1}=\frac{40}{2}
=20
$