0.4x=x^(1/3)

Solution for 0.4x=x^(1/3) equation:

x in (-oo:+oo)

0.4*x = x^(1/3) // - x^(1/3)

0.4*x-x^(1/3) = 0

t_1 = x^(1/3)

0.4*t_1^3-1*t_1^1 = 0

0.4*t_1^3-t_1 = 0

t_1*(0.4*t_1^2-1) = 0

0.4*t_1^2 = 1 // : 0.4

t_1^2 = 2.5

t_1^2 = 2.5 // ^ 1/2

abs(t_1) = 2.5^(1/2)

t_1 = 2.5^(1/2) or t_1 = -2.5^(1/2)

t_1 = 0

t_1 = 0

t_1 = 2.5^(1/2)

x^(1/3)-2.5^(1/2) = 0

1*x^(1/3) = 2.5^(1/2) // : 1

x^(1/3) = 2.5^(1/2)

x^(1/3) = 2.5^(1/2) // ^ 3

x = 2.5^(3/2)

t_1 = -2.5^(1/2)

x^(1/3)+2.5^(1/2) = 0

1*x^(1/3) = -2.5^(1/2) // : 1

x^(1/3) = -2.5^(1/2)

( -2.5^(1/2) < 0 i 1/3 in (0:1) ) => x należy do O

t_1 = 0

x^(1/3)+0 = 0

x^(1/3) = 0

1*x^(1/3) = 0 // : 1

x^(1/3) = 0

x = 0

x in { 2.5^(3/2), 0 }