x^(2/3)=7x^(1/3)-12

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Solution for x^(2/3)=7x^(1/3)-12 equation: 


x in (-oo:+oo)

x^(2/3) = 7*x^(1/3)-12 // - 7*x^(1/3)-12

x^(2/3)-(7*x^(1/3))+12 = 0

x^(2/3)-7*x^(1/3)+12 = 0

t_1 = x^(1/3)

1*t_1^2-7*t_1^1+12 = 0

t_1^2-7*t_1+12 = 0

DELTA = (-7)^2-(1*4*12)

DELTA = 1

DELTA > 0

t_1 = (1^(1/2)+7)/(1*2) or t_1 = (7-1^(1/2))/(1*2)

t_1 = 4 or t_1 = 3

t_1 = 3

x^(1/3)-3 = 0

1*x^(1/3) = 3 // : 1

x^(1/3) = 3

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

x = 27

t_1 = 4

x^(1/3)-4 = 0

1*x^(1/3) = 4 // : 1

x^(1/3) = 4

x^(1/3) = 4 // ^ 3

x = 64

x in { 27, 64 }

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