x^(2/5)=8x^(1/5)-15

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Solution for x^(2/5)=8x^(1/5)-15 equation: 


x in (-oo:+oo)

x^(2/5) = 8*x^(1/5)-15 // - 8*x^(1/5)-15

x^(2/5)-(8*x^(1/5))+15 = 0

x^(2/5)-8*x^(1/5)+15 = 0

t_1 = x^(1/5)

1*t_1^2-8*t_1^1+15 = 0

t_1^2-8*t_1+15 = 0

DELTA = (-8)^2-(1*4*15)

DELTA = 4

DELTA > 0

t_1 = (4^(1/2)+8)/(1*2) or t_1 = (8-4^(1/2))/(1*2)

t_1 = 5 or t_1 = 3

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

t_1 = 5

x^(1/5)-5 = 0

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

x^(1/5) = 5

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

x = 3125

x in { 243, 3125 }

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