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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

z^2-13z+40=0

a = 1; b = -13; c = +40;
Δ = b2-4ac
Δ = -132-4·1·40
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*1}=\frac{10}{2}
=5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3}{2*1}=\frac{16}{2}
=8
$