1-4/x-45/x^2=0

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Solution for 1-4/x-45/x^2=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)

1-(4/x)-(45/(x^2)) = 0

1-4*x^-1-45*x^-2 = 0

t_1 = x^-1

1-45*t_1^2-4*t_1^1 = 0

1-45*t_1^2-4*t_1 = 0

DELTA = (-4)^2-(-45*1*4)

DELTA = 196

DELTA > 0

t_1 = (196^(1/2)+4)/(-45*2) or t_1 = (4-196^(1/2))/(-45*2)

t_1 = -1/5 or t_1 = 1/9

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

t_1 = 1/9

x^-1-1/9 = 0

1*x^-1 = 1/9 // : 1

x^-1 = 1/9

-1 < 0

1/(x^1) = 1/9 // * x^1

1 = 1/9*x^1 // : 1/9

9 = x^1

x = 9

x in { -5, 9 }

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