1/3(1/5x-3)=1/2(2-1/x)

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Solution for 1/3(1/5x-3)=1/2(2-1/x) equation: 


D( x )

x = 0

x = 0

x = 0

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

(1/3)*((1/5)*x-3) = (1/2)*(2-(1/x)) // - (1/2)*(2-(1/x))

(1/3)*((1/5)*x-3)-((1/2)*(2-(1/x))) = 0

(1/3)*((1/5)*x-3)+(-1/2)*(2-x^-1) = 0

1/3*(1/5*x-3)-1/2*(2-x^-1) = 0

1/3*(1/5*x-3)-1/2*(2-x^-1) = 0

1/15*x+1/2*x^-1-2 = 0

1/15*x+1/2*x^-1-2 = 0

1/15*x^1+1/2*x^-1-2*x^0 = 0

(1/15*x^2-2*x^1+1/2*x^0)/(x^1) = 0 // * x^2

x^1*(1/15*x^2-2*x^1+1/2*x^0) = 0

x^1

(1/15)*x^2-2*x+1/2 = 0

(1/15)*x^2-2*x+1/2 = 0

DELTA = (-2)^2-(4*(1/15)*(1/2))

DELTA = 58/15

DELTA > 0

x = ((58/15)^(1/2)+2)/(2*(1/15)) or x = (2-(58/15)^(1/2))/(2*(1/15))

x = 15/2*((58/15)^(1/2)+2) or x = 15/2*(2-(58/15)^(1/2))

x in { 15/2*(2-(58/15)^(1/2)), 15/2*((58/15)^(1/2)+2)} 

(x-15/2*(2-(58/15)^(1/2)))*(x-15/2*((58/15)^(1/2)+2)) = 0

(x-15/2*(2-(58/15)^(1/2)))*(x-15/2*((58/15)^(1/2)+2)) = 0

( x-15/2*((58/15)^(1/2)+2) )

x-15/2*((58/15)^(1/2)+2) = 0 // + -15/2*((58/15)^(1/2)+2)

x = -(-15/2*((58/15)^(1/2)+2))

x = 15/2*((58/15)^(1/2)+2)

( x-15/2*(2-(58/15)^(1/2)) )

x-15/2*(2-(58/15)^(1/2)) = 0 // + -15/2*(2-(58/15)^(1/2))

x = -(-15/2*(2-(58/15)^(1/2)))

x = 15/2*(2-(58/15)^(1/2))

x in { 15/2*((58/15)^(1/2)+2), 15/2*(2-(58/15)^(1/2)) }

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