(z-8)(z-10)=0

Solution for (z-8)(z-10)=0 equation:

(z-8)(z-10)=0

We multiply parentheses ..

(+z^2-10z-8z+80)=0

We get rid of parentheses

z^2-10z-8z+80=0

We add all the numbers together, and all the variables

z^2-18z+80=0

a = 1; b = -18; c = +80;
Δ = b2-4ac
Δ = -182-4·1·80
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2}{2*1}=\frac{16}{2}
=8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2}{2*1}=\frac{20}{2}
=10
$