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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-5z^2+25z+z-5)=0

We get rid of parentheses

-5z^2+25z+z-5=0

We add all the numbers together, and all the variables

-5z^2+26z-5=0

a = -5; b = 26; c = -5;
Δ = b2-4ac
Δ = 262-4·(-5)·(-5)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-24}{2*-5}=\frac{-50}{-10}
=+5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+24}{2*-5}=\frac{-2}{-10}
=1/5
$