0.2k=0.5k^2

Solution for 0.2k=0.5k^2 equation:

0.2k=0.5k^2

We move all terms to the left:

0.2k-(0.5k^2)=0

We get rid of parentheses

-0.5k^2+0.2k=0

a = -0.5; b = 0.2; c = 0;
Δ = b2-4ac
Δ = 0.22-4·(-0.5)·0
Δ = 0.04
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.2)-\sqrt{0.04}}{2*-0.5}=\frac{-0.2-\sqrt{0.04}}{-1}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.2)+\sqrt{0.04}}{2*-0.5}=\frac{-0.2+\sqrt{0.04}}{-1}
$