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

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


x in (-oo:+oo)

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

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

t_1 = x^(1/3)

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

6*t_1^2-t_1-2 = 0

DELTA = (-1)^2-(-2*4*6)

DELTA = 49

DELTA > 0

t_1 = (49^(1/2)+1)/(2*6) or t_1 = (1-49^(1/2))/(2*6)

t_1 = 2/3 or t_1 = -1/2

t_1 = -1/2

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

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

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

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

t_1 = 2/3

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

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

x^(1/3) = 2/3

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

x = 8/27

x = 8/27

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