64k^2=4k

Solution for 64k^2=4k equation:

64k^2=4k

We move all terms to the left:

64k^2-(4k)=0

a = 64; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·64·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*64}=\frac{0}{128}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*64}=\frac{8}{128}
=1/16
$