(2x-6)^2/3=x^1/3

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Solution for (2x-6)^2/3=x^1/3 equation: 


x in (-oo:+oo)

((2*x-6)^2)/3 = (x^1)/3 // - (x^1)/3

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

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

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

(2*x-6)^2-x = 0

4*x^2-25*x+36 = 0

4*x^2-25*x+36 = 0

4*x^2-25*x+36 = 0

DELTA = (-25)^2-(4*4*36)

DELTA = 49

DELTA > 0

x = (49^(1/2)+25)/(2*4) or x = (25-49^(1/2))/(2*4)

x = 4 or x = 9/4

(x-9/4)*(x-4) = 0

((x-9/4)*(x-4))/3 = 0

((x-9/4)*(x-4))/3 = 0 // * 3

(x-9/4)*(x-4) = 0

( x-4 )

x-4 = 0 // + 4

x = 4

( x-9/4 )

x-9/4 = 0 // + 9/4

x = 9/4

x in { 4, 9/4 }

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