6k^2-64k+4=0

Solution for 6k^2-64k+4=0 equation:

6k^2-64k+4=0

a = 6; b = -64; c = +4;
Δ = b2-4ac
Δ = -642-4·6·4
Δ = 4000
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:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-20\sqrt{10}}{2*6}=\frac{64-20\sqrt{10}}{12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+20\sqrt{10}}{2*6}=\frac{64+20\sqrt{10}}{12}
$