(5z-2)(1-z)=0

Solution for (5z-2)(1-z)=0 equation:

(5z-2)(1-z)=0

We add all the numbers together, and all the variables

(5z-2)(-1z+1)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5z^2+7z-2=0

a = -5; b = 7; c = -2;
Δ = b2-4ac
Δ = 72-4·(-5)·(-2)
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{-(7)-3}{2*-5}=\frac{-10}{-10}
=1
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3}{2*-5}=\frac{-4}{-10}
=2/5
$