8z(z-6)=0

Solution for 8z(z-6)=0 equation:

8z(z-6)=0

We multiply parentheses

8z^2-48z=0

a = 8; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·8·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*8}=\frac{0}{16}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*8}=\frac{96}{16}
=6
$