0=8z^2-20z

Solution for 0=8z^2-20z equation:

0=8z^2-20z

We move all terms to the left:

0-(8z^2-20z)=0

We add all the numbers together, and all the variables

-(8z^2-20z)=0

We get rid of parentheses

-8z^2+20z=0

a = -8; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-8)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-8}=\frac{-40}{-16}
=2+1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-8}=\frac{0}{-16}
=0
$