x^(2/5)=5x^(1/5)-6

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Solution for x^(2/5)=5x^(1/5)-6 equation: 


x in (-oo:+oo)

x^(2/5) = 5*x^(1/5)-6 // - 5*x^(1/5)-6

x^(2/5)-(5*x^(1/5))+6 = 0

x^(2/5)-5*x^(1/5)+6 = 0

t_1 = x^(1/5)

1*t_1^2-5*t_1^1+6 = 0

t_1^2-5*t_1+6 = 0

DELTA = (-5)^2-(1*4*6)

DELTA = 1

DELTA > 0

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

t_1 = 3 or t_1 = 2

t_1 = 2

x^(1/5)-2 = 0

1*x^(1/5) = 2 // : 1

x^(1/5) = 2

x^(1/5) = 2 // ^ 5

x = 32

t_1 = 3

x^(1/5)-3 = 0

1*x^(1/5) = 3 // : 1

x^(1/5) = 3

x^(1/5) = 3 // ^ 5

x = 243

x in { 32, 243 }

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