(1/x)+(1/x-9)=(19/9x-33)

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Solution for (1/x)+(1/x-9)=(19/9x-33) equation: 


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

1/x+1/x-9 = (19/9)*x-33 // - (19/9)*x-33

1/x-((19/9)*x)+1/x-9+33 = 0

(-19/9)*x+1/x+1/x-9+33 = 0

2*x^-1-19/9*x^1+24*x^0 = 0

(24*x^1-19/9*x^2+2*x^0)/(x^1) = 0 // * x^2

x^1*(24*x^1-19/9*x^2+2*x^0) = 0

x^1

(-19/9)*x^2+24*x+2 = 0

(-19/9)*x^2+24*x+2 = 0

DELTA = 24^2-(2*4*(-19/9))

DELTA = 5336/9

DELTA > 0

x = ((5336/9)^(1/2)-24)/(2*(-19/9)) or x = (-(5336/9)^(1/2)-24)/(2*(-19/9))

x = -9/38*((5336/9)^(1/2)-24) or x = 9/38*((5336/9)^(1/2)+24)

x in { -9/38*((5336/9)^(1/2)-24), 9/38*((5336/9)^(1/2)+24)} 

x in { -9/38*((5336/9)^(1/2)-24), 9/38*((5336/9)^(1/2)+24) }

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