(5z-8)(1-z)=0

Solution for (5z-8)(1-z)=0 equation:

(5z-8)(1-z)=0

We add all the numbers together, and all the variables

(5z-8)(-1z+1)=0

We multiply parentheses ..

(-5z^2+5z+8z-8)=0

We get rid of parentheses

-5z^2+5z+8z-8=0

We add all the numbers together, and all the variables

-5z^2+13z-8=0

a = -5; b = 13; c = -8;
Δ = b2-4ac
Δ = 132-4·(-5)·(-8)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3}{2*-5}=\frac{-16}{-10}
=1+3/5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3}{2*-5}=\frac{-10}{-10}
=1
$