6x^-2/3-13x^-1/3-5

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Solution for 6x^-2/3-13x^-1/3-5 equation:


D( x )

x = 0

x = 0

x = 0

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

(6*x^-2)/3-((13*x^-1)/3)-5 = 0

(-13/3)*x^-1+(6*x^-2)/3-5 = 0

2*x^-2-13/3*x^-1-5 = 0

t_1 = x^-1

2*t_1^2-13/3*t_1^1-5 = 0

2*t_1^2-13/3*t_1-5 = 0

DELTA = (-13/3)^2-(-5*2*4)

DELTA = 529/9

DELTA > 0

t_1 = ((529/9)^(1/2)+13/3)/(2*2) or t_1 = (13/3-(529/9)^(1/2))/(2*2)

t_1 = 3 or t_1 = -5/6

t_1 = -5/6

x^-1+5/6 = 0

1*x^-1 = -5/6 // : 1

x^-1 = -5/6

-1 < 0

1/(x^1) = -5/6 // * x^1

1 = -5/6*x^1 // : -5/6

-6/5 = x^1

x = -6/5

t_1 = 3

x^-1-3 = 0

1*x^-1 = 3 // : 1

x^-1 = 3

-1 < 0

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

1 = 3*x^1 // : 3

1/3 = x^1

x = 1/3

x in { -6/5, 1/3 }

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