0.0625k+0.25k(k-0.25)=0

Solution for 0.0625k+0.25k(k-0.25)=0 equation:

0.0625k+0.25k(k-0.25)=0

We multiply parentheses

0k^2+0.0625k-0k=0

We add all the numbers together, and all the variables

k^2-0.9375k=0

a = 1; b = -0.9375; c = 0;
Δ = b2-4ac
Δ = -0.93752-4·1·0
Δ = 0.87890625
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{-(-0.9375)-\sqrt{0.87890625}}{2*1}=\frac{0.9375-\sqrt{0.87890625}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.9375)+\sqrt{0.87890625}}{2*1}=\frac{0.9375+\sqrt{0.87890625}}{2}
$