k^2-2k=111=9

Solution for k^2-2k=111=9 equation:

k^2-2k=111=9

We move all terms to the left:

k^2-2k-(111)=0

a = 1; b = -2; c = -111;
Δ = b2-4ac
Δ = -22-4·1·(-111)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8\sqrt{7}}{2*1}=\frac{2-8\sqrt{7}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8\sqrt{7}}{2*1}=\frac{2+8\sqrt{7}}{2}
$