(x-2)^2/3=x^1/3

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Solution for (x-2)^2/3=x^1/3 equation: 


x in (-oo:+oo)

((x-2)^2)/3 = (x^1)/3 // - (x^1)/3

((x-2)^2)/3-((x^1)/3) = 0

((x-2)^2)/3-(x/3) = 0

((x-2)^2)/3-x/3 = 0

(x-2)^2-x = 0

x^2-5*x+4 = 0

x^2-5*x+4 = 0

x^2-5*x+4 = 0

DELTA = (-5)^2-(1*4*4)

DELTA = 9

DELTA > 0

x = (9^(1/2)+5)/(1*2) or x = (5-9^(1/2))/(1*2)

x = 4 or x = 1

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

((x-1)*(x-4))/3 = 0

((x-1)*(x-4))/3 = 0 // * 3

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

( x-1 )

x-1 = 0 // + 1

x = 1

( x-4 )

x-4 = 0 // + 4

x = 4

x in { 1, 4 }

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