8/x+15/x^2=-1

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Solution for 8/x+15/x^2=-1 equation: 


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

8/x+15/(x^2) = -1 // + 1

8/x+15/(x^2)+1 = 0

8*x^-1+15*x^-2+1 = 0

t_1 = x^-1

15*t_1^2+8*t_1^1+1 = 0

15*t_1^2+8*t_1+1 = 0

DELTA = 8^2-(1*4*15)

DELTA = 4

DELTA > 0

t_1 = (4^(1/2)-8)/(2*15) or t_1 = (-4^(1/2)-8)/(2*15)

t_1 = -1/5 or t_1 = -1/3

t_1 = -1/3

x^-1+1/3 = 0

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

x^-1 = -1/3

-1 < 0

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

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

-3 = x^1

x = -3

t_1 = -1/5

x^-1+1/5 = 0

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

x^-1 = -1/5

-1 < 0

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

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

-5 = x^1

x = -5

x in { -3, -5 }

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