2-9/x^2=5/x

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Solution for 2-9/x^2=5/x 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)

2-(9/(x^2)) = 5/x // - 5/x

2-(5/x)-(9/(x^2)) = 0

2-5*x^-1-9*x^-2 = 0

t_1 = x^-1

2-9*t_1^2-5*t_1^1 = 0

2-9*t_1^2-5*t_1 = 0

DELTA = (-5)^2-(-9*2*4)

DELTA = 97

DELTA > 0

t_1 = (97^(1/2)+5)/(-9*2) or t_1 = (5-97^(1/2))/(-9*2)

t_1 = (97^(1/2)+5)/(-18) or t_1 = (5-97^(1/2))/(-18)

t_1 = (97^(1/2)+5)/(-18)

x^-1-((97^(1/2)+5)/(-18)) = 0

1*x^-1 = (97^(1/2)+5)/(-18) // : 1

x^-1 = (97^(1/2)+5)/(-18)

-1 < 0

1/(x^1) = (97^(1/2)+5)/(-18) // * x^1

1 = ((97^(1/2)+5)/(-18))*x^1 // : (97^(1/2)+5)/(-18)

-18*(97^(1/2)+5)^-1 = x^1

x = -18*(97^(1/2)+5)^-1

t_1 = (5-97^(1/2))/(-18)

x^-1-((5-97^(1/2))/(-18)) = 0

1*x^-1 = (5-97^(1/2))/(-18) // : 1

x^-1 = (5-97^(1/2))/(-18)

-1 < 0

1/(x^1) = (5-97^(1/2))/(-18) // * x^1

1 = ((5-97^(1/2))/(-18))*x^1 // : (5-97^(1/2))/(-18)

-18*(5-97^(1/2))^-1 = x^1

x = -18*(5-97^(1/2))^-1

x in { -18*(97^(1/2)+5)^-1, -18*(5-97^(1/2))^-1 }

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