n^2-6n+5=16^2

Solution for n^2-6n+5=16^2 equation:

n^2-6n+5=16^2

We move all terms to the left:

n^2-6n+5-(16^2)=0

We add all the numbers together, and all the variables

n^2-6n-251=0

a = 1; b = -6; c = -251;
Δ = b2-4ac
Δ = -62-4·1·(-251)
Δ = 1040
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:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{65}}{2*1}=\frac{6-4\sqrt{65}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{65}}{2*1}=\frac{6+4\sqrt{65}}{2}
$