5x^(2/3)-39x^(1/3)-8=0

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Solution for 5x^(2/3)-39x^(1/3)-8=0 equation: 


x in (-oo:+oo)

5*x^(2/3)-(39*x^(1/3))-8 = 0

5*x^(2/3)-39*x^(1/3)-8 = 0

t_1 = x^(1/3)

5*t_1^2-39*t_1^1-8 = 0

5*t_1^2-39*t_1-8 = 0

DELTA = (-39)^2-(-8*4*5)

DELTA = 1681

DELTA > 0

t_1 = (1681^(1/2)+39)/(2*5) or t_1 = (39-1681^(1/2))/(2*5)

t_1 = 8 or t_1 = -1/5

t_1 = -1/5

x^(1/3)+1/5 = 0

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

x^(1/3) = -1/5

( -1/5 < 0 i 1/3 in (0:1) ) => x należy do O

t_1 = 8

x^(1/3)-8 = 0

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

x^(1/3) = 8

x^(1/3) = 8 // ^ 3

x = 512

x = 512

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