n^2-18n=80

Solution for n^2-18n=80 equation:

n^2-18n=80

We move all terms to the left:

n^2-18n-(80)=0

a = 1; b = -18; c = -80;
Δ = b2-4ac
Δ = -182-4·1·(-80)
Δ = 644
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:

$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{161}}{2*1}=\frac{18-2\sqrt{161}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{161}}{2*1}=\frac{18+2\sqrt{161}}{2}
$