k^2-6k=11

Solution for k^2-6k=11 equation:

k^2-6k=11

We move all terms to the left:

k^2-6k-(11)=0

a = 1; b = -6; c = -11;
Δ = b2-4ac
Δ = -62-4·1·(-11)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{5}}{2*1}=\frac{6-4\sqrt{5}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{5}}{2*1}=\frac{6+4\sqrt{5}}{2}
$