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

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

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

We multiply parentheses ..

4(+x^2+2x-8x-16)=0

We multiply parentheses

4x^2+8x-32x-64=0

We add all the numbers together, and all the variables

4x^2-24x-64=0

a = 4; b = -24; c = -64;
Δ = b2-4ac
Δ = -242-4·4·(-64)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-40}{2*4}=\frac{-16}{8}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+40}{2*4}=\frac{64}{8}
=8
$