((2x-6)/x)=((x-2)/4)

Solution for ((2x-6)/x)=((x-2)/4) equation:

D( x )

x = 0

x = 0

x = 0

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

(2*x-6)/x = (x-2)/4 // - (x-2)/4

(2*x-6)/x-((x-2)/4) = 0

(2*x-6)/x+(-1*(x-2))/4 = 0

(4*(2*x-6))/(4*x)+(-1*x*(x-2))/(4*x) = 0

4*(2*x-6)-1*x*(x-2) = 0

10*x-x^2-24 = 0

10*x-x^2-24 = 0

10*x-x^2-24 = 0

DELTA = 10^2-(-24*(-1)*4)

DELTA = 4

DELTA > 0

x = (4^(1/2)-10)/(-1*2) or x = (-4^(1/2)-10)/(-1*2)

x = 4 or x = 6

(x-4)*(x-6) = 0

((x-4)*(x-6))/(4*x) = 0

((x-4)*(x-6))/(4*x) = 0 // * 4*x

(x-4)*(x-6) = 0

( x-4 )

x-4 = 0 // + 4

x = 4

( x-6 )

x-6 = 0 // + 6

x = 6

x in { 4, 6 }