1/x^2+9/x+20=0

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Solution for 1/x^2+9/x+20=0 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)

9/x+1/(x^2)+20 = 0

9*x^-1+x^-2+20 = 0

t_1 = x^-1

1*t_1^2+9*t_1^1+20 = 0

t_1^2+9*t_1+20 = 0

DELTA = 9^2-(1*4*20)

DELTA = 1

DELTA > 0

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

t_1 = -4 or t_1 = -5

t_1 = -5

x^-1+5 = 0

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

x^-1 = -5

-1 < 0

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

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

-1/5 = x^1

x = -1/5

t_1 = -4

x^-1+4 = 0

1*x^-1 = -4 // : 1

x^-1 = -4

-1 < 0

1/(x^1) = -4 // * x^1

1 = -4*x^1 // : -4

-1/4 = x^1

x = -1/4

x in { -1/5, -1/4 }

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