5-1/x-4/x^2=0

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Solution for 5-1/x-4/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)

5-(1/x)-(4/(x^2)) = 0

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

t_1 = x^-1

5-4*t_1^2-1*t_1^1 = 0

5-4*t_1^2-t_1 = 0

DELTA = (-1)^2-(-4*4*5)

DELTA = 81

DELTA > 0

t_1 = (81^(1/2)+1)/(-4*2) or t_1 = (1-81^(1/2))/(-4*2)

t_1 = -5/4 or t_1 = 1

t_1 = -5/4

x^-1+5/4 = 0

1*x^-1 = -5/4 // : 1

x^-1 = -5/4

-1 < 0

1/(x^1) = -5/4 // * x^1

1 = -5/4*x^1 // : -5/4

-4/5 = x^1

x = -4/5

t_1 = 1

x^-1-1 = 0

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

x^-1 = 1

-1 < 0

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

1 = 1*x^1 // : 1

1 = x^1

x = 1

x in { -4/5, 1 }

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