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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses

2x^2-3x^2-8x+6x=0

We add all the numbers together, and all the variables

-1x^2-2x=0

a = -1; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-1)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-1}=\frac{4}{-2}
=-2
$