n^2-11n+1=0

Solution for n^2-11n+1=0 equation:

n^2-11n+1=0

a = 1; b = -11; c = +1;
Δ = b2-4ac
Δ = -112-4·1·1
Δ = 117
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:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-3\sqrt{13}}{2*1}=\frac{11-3\sqrt{13}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+3\sqrt{13}}{2*1}=\frac{11+3\sqrt{13}}{2}
$