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

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

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

We move all terms to the left:

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

determiningTheFunctionDomain
2x(x-4)-32x=0

We add all the numbers together, and all the variables

-32x+2x(x-4)=0

We multiply parentheses

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

We add all the numbers together, and all the variables

2x^2-40x=0

a = 2; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·2·0
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{-(-40)-40}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*2}=\frac{80}{4}
=20
$