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

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

x in (-oo:+oo)

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

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

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

t_1 = x^(2/3)

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

t_1^2-10*t_1+9 = 0

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

DELTA = 64

DELTA > 0

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

t_1 = 9 or t_1 = 1

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

t_1 = 9

x^(2/3)-9 = 0

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

x^(2/3) = 9

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

x^2 = 729 // ^ 1/2

abs(x) = 27

x = 27 or x = -27

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