2(x-4)((200/x)-4)=192

Solution for 2(x-4)((200/x)-4)=192 equation:

D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

2*(x-4)*(200/x-4) = 192 // - 192

2*(x-4)*(200/x-4)-192 = 0

2*(x-4)*(200*x^-1-4)-192 = 0

2*(x-4)*(200*x^-1-4)-192 = 0

240-8*x-1600*x^-1 = 0

240-8*x-1600*x^-1 = 0

8*(30-x-200*x^-1) = 0

30*x^0-1*x^1-200*x^-1 = 0

(30*x^1-1*x^2-200*x^0)/(x^1) = 0 // * x^2

x^1*(30*x^1-1*x^2-200*x^0) = 0

x^1

30*x-x^2-200 = 0

30*x-x^2-200 = 0

DELTA = 30^2-(-200*(-1)*4)

DELTA = 100

DELTA > 0

x = (100^(1/2)-30)/(-1*2) or x = (-100^(1/2)-30)/(-1*2)

x = 10 or x = 20

x in { 10, 20} 

8*(x-10)*(x-20) = 0

8*(x-10)*(x-20) = 0

( 8 )

8 = 0

x belongs to the empty set

( x-10 )

x-10 = 0 // + 10

x = 10

( x-20 )

x-20 = 0 // + 20

x = 20

x in { 10, 20 }