5k(k-1)=10

Solution for 5k(k-1)=10 equation:

5k(k-1)=10

We move all terms to the left:

5k(k-1)-(10)=0

We multiply parentheses

5k^2-5k-10=0

a = 5; b = -5; c = -10;
Δ = b2-4ac
Δ = -52-4·5·(-10)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-15}{2*5}=\frac{-10}{10}
=-1
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+15}{2*5}=\frac{20}{10}
=2
$