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

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Solution for 4/x-45/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)

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

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

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

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

t_1 = x^-1

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

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

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

DELTA = 196

DELTA > 0

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

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

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

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 { -9, 5 }

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