8k^2-16k=16

Solution for 8k^2-16k=16 equation:

8k^2-16k=16

We move all terms to the left:

8k^2-16k-(16)=0

a = 8; b = -16; c = -16;
Δ = b2-4ac
Δ = -162-4·8·(-16)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16\sqrt{3}}{2*8}=\frac{16-16\sqrt{3}}{16}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16\sqrt{3}}{2*8}=\frac{16+16\sqrt{3}}{16}
$