(8x-20)(4x-1)=0

Solution for (8x-20)(4x-1)=0 equation:

(8x-20)(4x-1)=0

We multiply parentheses ..

(+32x^2-8x-80x+20)=0

We get rid of parentheses

32x^2-8x-80x+20=0

We add all the numbers together, and all the variables

32x^2-88x+20=0

a = 32; b = -88; c = +20;
Δ = b2-4ac
Δ = -882-4·32·20
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-72}{2*32}=\frac{16}{64}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+72}{2*32}=\frac{160}{64}
=2+1/2
$