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

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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 $

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