8x^(2/3)-9x^(1/3)+1=0

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Solution for 8x^(2/3)-9x^(1/3)+1=0 equation: 


x in (-oo:+oo)

8*x^(2/3)-(9*x^(1/3))+1 = 0

8*x^(2/3)-9*x^(1/3)+1 = 0

t_1 = x^(1/3)

8*t_1^2-9*t_1^1+1 = 0

8*t_1^2-9*t_1+1 = 0

DELTA = (-9)^2-(1*4*8)

DELTA = 49

DELTA > 0

t_1 = (49^(1/2)+9)/(2*8) or t_1 = (9-49^(1/2))/(2*8)

t_1 = 1 or t_1 = 1/8

t_1 = 1/8

x^(1/3)-1/8 = 0

1*x^(1/3) = 1/8 // : 1

x^(1/3) = 1/8

x^(1/3) = 1/8 // ^ 3

x = 1/512

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

x in { 1/512, 1 }

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