2(x-4)((340/x)-4)=416

Solution for 2(x-4)((340/x)-4)=416 equation:

D( x )

x = 0

x = 0

x = 0

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

2*(x-4)*(340/x-4) = 416 // - 416

2*(x-4)*(340/x-4)-416 = 0

2*(x-4)*(340*x^-1-4)-416 = 0

2*(x-4)*(340*x^-1-4)-416 = 0

296-8*x-2720*x^-1 = 0

296-8*x-2720*x^-1 = 0

8*(37-x-340*x^-1) = 0

37*x^0-1*x^1-340*x^-1 = 0

(37*x^1-1*x^2-340*x^0)/(x^1) = 0 // * x^2

x^1*(37*x^1-1*x^2-340*x^0) = 0

x^1

37*x-x^2-340 = 0

37*x-x^2-340 = 0

DELTA = 37^2-(-340*(-1)*4)

DELTA = 9

DELTA > 0

x = (9^(1/2)-37)/(-1*2) or x = (-9^(1/2)-37)/(-1*2)

x = 17 or x = 20

x in { 17, 20} 

8*(x-17)*(x-20) = 0

8*(x-17)*(x-20) = 0

( x-17 )

x-17 = 0 // + 17

x = 17

( x-20 )

x-20 = 0 // + 20

x = 20

x in { 17, 20 }