x^(4/3)-13x^(2/3)+40=0

Solution for x^(4/3)-13x^(2/3)+40=0 equation:

x in (-oo:+oo)

x^(4/3)-(13*x^(2/3))+40 = 0

x^(4/3)-13*x^(2/3)+40 = 0

t_1 = x^(2/3)

1*t_1^2-13*t_1^1+40 = 0

t_1^2-13*t_1+40 = 0

DELTA = (-13)^2-(1*4*40)

DELTA = 9

DELTA > 0

t_1 = (9^(1/2)+13)/(1*2) or t_1 = (13-9^(1/2))/(1*2)

t_1 = 8 or t_1 = 5

t_1 = 5

x^(2/3)-5 = 0

1*x^(2/3) = 5 // : 1

x^(2/3) = 5

x^(2/3) = 5 // ^ 3

x^2 = 125 // ^ 1/2

abs(x) = 5*5^(1/2)

x = 5*5^(1/2) or x = -(5*5^(1/2))

t_1 = 8

x^(2/3)-8 = 0

1*x^(2/3) = 8 // : 1

x^(2/3) = 8

x^(2/3) = 8 // ^ 3

x^2 = 512 // ^ 1/2

abs(x) = 16*2^(1/2)

x = 16*2^(1/2) or x = -(16*2^(1/2))

x in { 5*5^(1/2), -(5*5^(1/2)), 16*2^(1/2), -(16*2^(1/2)) }