k^2-11k-1=0

Solution for k^2-11k-1=0 equation:

k^2-11k-1=0

a = 1; b = -11; c = -1;
Δ = b2-4ac
Δ = -112-4·1·(-1)
Δ = 125
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5\sqrt{5}}{2*1}=\frac{11-5\sqrt{5}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5\sqrt{5}}{2*1}=\frac{11+5\sqrt{5}}{2}
$