n^2+2n+5=85

Solution for n^2+2n+5=85 equation:

n^2+2n+5=85

We move all terms to the left:

n^2+2n+5-(85)=0

We add all the numbers together, and all the variables

n^2+2n-80=0

a = 1; b = 2; c = -80;
Δ = b2-4ac
Δ = 22-4·1·(-80)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-18}{2*1}=\frac{-20}{2}
=-10
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+18}{2*1}=\frac{16}{2}
=8
$