8k^2-72k+44=0

Solution for 8k^2-72k+44=0 equation:

8k^2-72k+44=0

a = 8; b = -72; c = +44;
Δ = b2-4ac
Δ = -722-4·8·44
Δ = 3776
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:

$\sqrt{\Delta}=\sqrt{3776}=\sqrt{64*59}=\sqrt{64}*\sqrt{59}=8\sqrt{59}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{59}}{2*8}=\frac{72-8\sqrt{59}}{16}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{59}}{2*8}=\frac{72+8\sqrt{59}}{16}
$