x^(2/3)=5x^(1/3)-4

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Solution for x^(2/3)=5x^(1/3)-4 equation: 


x in (-oo:+oo)

x^(2/3) = 5*x^(1/3)-4 // - 5*x^(1/3)-4

x^(2/3)-(5*x^(1/3))+4 = 0

x^(2/3)-5*x^(1/3)+4 = 0

t_1 = x^(1/3)

1*t_1^2-5*t_1^1+4 = 0

t_1^2-5*t_1+4 = 0

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

DELTA = 9

DELTA > 0

t_1 = (9^(1/2)+5)/(1*2) or t_1 = (5-9^(1/2))/(1*2)

t_1 = 4 or t_1 = 1

t_1 = 1

x^(1/3)-1 = 0

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

x^(1/3) = 1

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

x = 1

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 { 1, 64 }

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