n^2+16=18n

Solution for n^2+16=18n equation:

n^2+16=18n

We move all terms to the left:

n^2+16-(18n)=0

a = 1; b = -18; c = +16;
Δ = b2-4ac
Δ = -182-4·1·16
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{65}}{2*1}=\frac{18-2\sqrt{65}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{65}}{2*1}=\frac{18+2\sqrt{65}}{2}
$