x/3(x-1)+1=x

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Solution for x/3(x-1)+1=x equation: 


x in (-oo:+oo)

(x/3)*(x-1)+1 = x // - x

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

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

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

1/3*x^2-4/3*x+1 = 0

1/3*x^2-4/3*x+1 = 0

1/3*x^2-4/3*x+1 = 0

DELTA = (-4/3)^2-(1/3*1*4)

DELTA = 4/9

DELTA > 0

x = ((4/9)^(1/2)+4/3)/(1/3*2) or x = (4/3-(4/9)^(1/2))/(1/3*2)

x = 3 or x = 1

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

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

( x-1 )

x-1 = 0 // + 1

x = 1

( x-3 )

x-3 = 0 // + 3

x = 3

x in { 1, 3 }

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