(2x-6)/(x)=(x-3)/(3)

Solution for (2x-6)/(x)=(x-3)/(3) equation:

D( x )

x = 0

x = 0

x = 0

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

(2*x-6)/x = (x-3)/3 // - (x-3)/3

(2*x-6)/x-((x-3)/3) = 0

(2*x-6)/x+(-1*(x-3))/3 = 0

(3*(2*x-6))/(3*x)+(-1*x*(x-3))/(3*x) = 0

3*(2*x-6)-1*x*(x-3) = 0

9*x-x^2-18 = 0

9*x-x^2-18 = 0

9*x-x^2-18 = 0

DELTA = 9^2-(-18*(-1)*4)

DELTA = 9

DELTA > 0

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

x = 3 or x = 6

(x-3)*(x-6) = 0

((x-3)*(x-6))/(3*x) = 0

((x-3)*(x-6))/(3*x) = 0 // * 3*x

(x-3)*(x-6) = 0

( x-3 )

x-3 = 0 // + 3

x = 3

( x-6 )

x-6 = 0 // + 6

x = 6

x in { 3, 6 }