(x-4)((160/x)-4)(2)=144

Solution for (x-4)((160/x)-4)(2)=144 equation:

D( x )

x = 0

x = 0

x = 0

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

2*(x-4)*(160/x-4) = 144 // - 144

2*(x-4)*(160/x-4)-144 = 0

2*(x-4)*(160*x^-1-4)-144 = 0

2*(x-4)*(160*x^-1-4)-144 = 0

208-8*x-1280*x^-1 = 0

208-8*x-1280*x^-1 = 0

8*(26-x-160*x^-1) = 0

26*x^0-1*x^1-160*x^-1 = 0

(26*x^1-1*x^2-160*x^0)/(x^1) = 0 // * x^2

x^1*(26*x^1-1*x^2-160*x^0) = 0

x^1

26*x-x^2-160 = 0

26*x-x^2-160 = 0

DELTA = 26^2-(-160*(-1)*4)

DELTA = 36

DELTA > 0

x = (36^(1/2)-26)/(-1*2) or x = (-36^(1/2)-26)/(-1*2)

x = 10 or x = 16

x in { 10, 16} 

8*(x-10)*(x-16) = 0

8*(x-10)*(x-16) = 0

( 8 )

8 = 0

x belongs to the empty set

( x-10 )

x-10 = 0 // + 10

x = 10

( x-16 )

x-16 = 0 // + 16

x = 16

x in { 10, 16 }