9x^(2/3)-71x^(1/3)-8=0

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Solution for 9x^(2/3)-71x^(1/3)-8=0 equation: 


x in (-oo:+oo)

9*x^(2/3)-(71*x^(1/3))-8 = 0

9*x^(2/3)-71*x^(1/3)-8 = 0

t_1 = x^(1/3)

9*t_1^2-71*t_1^1-8 = 0

9*t_1^2-71*t_1-8 = 0

DELTA = (-71)^2-(-8*4*9)

DELTA = 5329

DELTA > 0

t_1 = (5329^(1/2)+71)/(2*9) or t_1 = (71-5329^(1/2))/(2*9)

t_1 = 8 or t_1 = -1/9

t_1 = -1/9

x^(1/3)+1/9 = 0

1*x^(1/3) = -1/9 // : 1

x^(1/3) = -1/9

( -1/9 < 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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