9x^(4/3)-10x^(2/3)+1=0

Solution for 9x^(4/3)-10x^(2/3)+1=0 equation:

x in (-oo:+oo)

9*x^(4/3)-(10*x^(2/3))+1 = 0

9*x^(4/3)-10*x^(2/3)+1 = 0

t_1 = x^(2/3)

9*t_1^2-10*t_1^1+1 = 0

9*t_1^2-10*t_1+1 = 0

DELTA = (-10)^2-(1*4*9)

DELTA = 64

DELTA > 0

t_1 = (64^(1/2)+10)/(2*9) or t_1 = (10-64^(1/2))/(2*9)

t_1 = 1 or t_1 = 1/9

t_1 = 1/9

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

1*x^(2/3) = 1/9 // : 1

x^(2/3) = 1/9

x^(2/3) = 1/9 // ^ 3

x^2 = 1/729 // ^ 1/2

abs(x) = 1/27

x = 1/27 or x = -1/27

t_1 = 1

x^(2/3)-1 = 0

1*x^(2/3) = 1 // : 1

x^(2/3) = 1

x^(2/3) = 1 // ^ 3

x^2 = 1 // ^ 1/2

abs(x) = 1

x = 1 or x = -1

x in { 1/27, -1/27, 1, -1 }