0=400*(20-x)*(x-4)

Solution for 0=400*(20-x)*(x-4) equation:

0=400(20-x)(x-4)

We move all terms to the left:

0-(400(20-x)(x-4))=0

We add all the numbers together, and all the variables

-(400(-1x+20)(x-4))+0=0

We add all the numbers together, and all the variables

-(400(-1x+20)(x-4))=0

We multiply parentheses ..

-(400(-1x^2+4x+20x-80))=0


We calculate terms in parentheses: -(400(-1x^2+4x+20x-80)), so:

400(-1x^2+4x+20x-80)

We multiply parentheses

-400x^2+1600x+8000x-32000

We add all the numbers together, and all the variables

-400x^2+9600x-32000

Back to the equation:

-(-400x^2+9600x-32000)


We get rid of parentheses

400x^2-9600x+32000=0

a = 400; b = -9600; c = +32000;
Δ = b2-4ac
Δ = -96002-4·400·32000
Δ = 40960000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40960000}=6400$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9600)-6400}{2*400}=\frac{3200}{800}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9600)+6400}{2*400}=\frac{16000}{800}
=20
$