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

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


x in (-oo:+oo)

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

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

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

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

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

36*x^2-13*x+1 = 0

36*x^2-13*x+1 = 0

36*x^2-13*x+1 = 0

DELTA = (-13)^2-(1*4*36)

DELTA = 25

DELTA > 0

x = (25^(1/2)+13)/(2*36) or x = (13-25^(1/2))/(2*36)

x = 1/4 or x = 1/9

(x-1/9)*(x-1/4) = 0

((x-1/9)*(x-1/4))/3 = 0

((x-1/9)*(x-1/4))/3 = 0 // * 3

(x-1/9)*(x-1/4) = 0

( x-1/4 )

x-1/4 = 0 // + 1/4

x = 1/4

( x-1/9 )

x-1/9 = 0 // + 1/9

x = 1/9

x in { 1/4, 1/9 }

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