k(k-2)=5

Solution for k(k-2)=5 equation:

k(k-2)=5

We move all terms to the left:

k(k-2)-(5)=0

We multiply parentheses

k^2-2k-5=0

a = 1; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·1·(-5)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{6}}{2*1}=\frac{2-2\sqrt{6}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{6}}{2*1}=\frac{2+2\sqrt{6}}{2}
$