(x-8)(2x-10)=0

Solution for (x-8)(2x-10)=0 equation:

(x-8)(2x-10)=0

We multiply parentheses ..

(+2x^2-10x-16x+80)=0

We get rid of parentheses

2x^2-10x-16x+80=0

We add all the numbers together, and all the variables

2x^2-26x+80=0

a = 2; b = -26; c = +80;
Δ = b2-4ac
Δ = -262-4·2·80
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-6}{2*2}=\frac{20}{4}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+6}{2*2}=\frac{32}{4}
=8
$