x^(4/3)-5x^(2/3)+6=0

Solution for x^(4/3)-5x^(2/3)+6=0 equation:

x in (-oo:+oo)

x^(4/3)-(5*x^(2/3))+6 = 0

x^(4/3)-5*x^(2/3)+6 = 0

t_1 = x^(2/3)

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^(2/3)-2 = 0

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

x^(2/3) = 2

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

x^2 = 8 // ^ 1/2

abs(x) = 2*2^(1/2)

x = 2*2^(1/2) or x = -(2*2^(1/2))

t_1 = 3

x^(2/3)-3 = 0

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

x^(2/3) = 3

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

x^2 = 27 // ^ 1/2

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

x = 3*3^(1/2) or x = -(3*3^(1/2))

x in { 2*2^(1/2), -(2*2^(1/2)), 3*3^(1/2), -(3*3^(1/2)) }