n2-12n+1=0

Solution for n2-12n+1=0 equation:

n2-12n+1=0

We add all the numbers together, and all the variables

n^2-12n+1=0

a = 1; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·1·1
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{35}}{2*1}=\frac{12-2\sqrt{35}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{35}}{2*1}=\frac{12+2\sqrt{35}}{2}
$