(4x-8)(5x-2)=0

Solution for (4x-8)(5x-2)=0 equation:

(4x-8)(5x-2)=0

We multiply parentheses ..

(+20x^2-8x-40x+16)=0

We get rid of parentheses

20x^2-8x-40x+16=0

We add all the numbers together, and all the variables

20x^2-48x+16=0

a = 20; b = -48; c = +16;
Δ = b2-4ac
Δ = -482-4·20·16
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-32}{2*20}=\frac{16}{40}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+32}{2*20}=\frac{80}{40}
=2
$