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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

x^2-12x+32=0

a = 1; b = -12; c = +32;
Δ = b2-4ac
Δ = -122-4·1·32
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4}{2*1}=\frac{8}{2}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4}{2*1}=\frac{16}{2}
=8
$