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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-5z^2+8z+25z-40)=0

We get rid of parentheses

-5z^2+8z+25z-40=0

We add all the numbers together, and all the variables

-5z^2+33z-40=0

a = -5; b = 33; c = -40;
Δ = b2-4ac
Δ = 332-4·(-5)·(-40)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-17}{2*-5}=\frac{-50}{-10}
=+5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+17}{2*-5}=\frac{-16}{-10}
=1+3/5
$