2x^(-2/3)-7x^(-1/3)-15=0

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Solution for 2x^(-2/3)-7x^(-1/3)-15=0 equation: 


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

2*x^(-2/3)-(7*x^(-1/3))-15 = 0

2*x^(-2/3)-7*x^(-1/3)-15 = 0

t_1 = x^(-1/3)

2*t_1^2-7*t_1^1-15 = 0

2*t_1^2-7*t_1-15 = 0

DELTA = (-7)^2-(-15*2*4)

DELTA = 169

DELTA > 0

t_1 = (169^(1/2)+7)/(2*2) or t_1 = (7-169^(1/2))/(2*2)

t_1 = 5 or t_1 = -3/2

t_1 = -3/2

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

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

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

-1/3 < 0

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

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

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

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

x = -8/27

t_1 = 5

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

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

x^(-1/3) = 5

-1/3 < 0

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

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

1/5 = x^(1/3)

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

x = 1/125

x in { -8/27, 1/125 }

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