-4k^2-8k(8k+1)=0

Solution for -4k^2-8k(8k+1)=0 equation:

-4k^2-8k(8k+1)=0

We multiply parentheses

-4k^2-64k^2-8k=0

We add all the numbers together, and all the variables

-68k^2-8k=0

a = -68; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-68)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-68}=\frac{0}{-136}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-68}=\frac{16}{-136}
=-2/17
$