24x^(2/3)-6x^(1/3)-3=0

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Solution for 24x^(2/3)-6x^(1/3)-3=0 equation: 


x in (-oo:+oo)

24*x^(2/3)-(6*x^(1/3))-3 = 0

24*x^(2/3)-6*x^(1/3)-3 = 0

t_1 = x^(1/3)

24*t_1^2-6*t_1^1-3 = 0

24*t_1^2-6*t_1-3 = 0

DELTA = (-6)^2-(-3*4*24)

DELTA = 324

DELTA > 0

t_1 = (324^(1/2)+6)/(2*24) or t_1 = (6-324^(1/2))/(2*24)

t_1 = 1/2 or t_1 = -1/4

t_1 = -1/4

x^(1/3)+1/4 = 0

1*x^(1/3) = -1/4 // : 1

x^(1/3) = -1/4

( -1/4 < 0 i 1/3 in (0:1) ) => x należy do O

t_1 = 1/2

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

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

x^(1/3) = 1/2

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

x = 1/8

x = 1/8

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