8z(8z+1)=0

Solution for 8z(8z+1)=0 equation:

8z(8z+1)=0

We multiply parentheses

64z^2+8z=0

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

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