4x(8-x)-(3x-2)(8-x)=0

Solution for 4x(8-x)-(3x-2)(8-x)=0 equation:

4x(8-x)-(3x-2)(8-x)=0

We add all the numbers together, and all the variables

4x(-1x+8)-(3x-2)(-1x+8)=0

We multiply parentheses

-4x^2+32x-(3x-2)(-1x+8)=0

We multiply parentheses ..

-4x^2-(-3x^2+24x+2x-16)+32x=0

We get rid of parentheses

-4x^2+3x^2-24x-2x+32x+16=0

We add all the numbers together, and all the variables

-1x^2+6x+16=0

a = -1; b = 6; c = +16;
Δ = b2-4ac
Δ = 62-4·(-1)·16
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10}{2*-1}=\frac{-16}{-2}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10}{2*-1}=\frac{4}{-2}
=-2
$