(1/2x)+(3/x+7)=(-1/x)

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Solution for (1/2x)+(3/x+7)=(-1/x) equation: 


D( x )

x = 0

x = 0

x = 0

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

(1/2)*x+3/x+7 = -1/x // + -1/x

(1/2)*x+3/x-(-1/x)+7 = 0

(1/2)*x+3/x+x^-1+7 = 0

1/2*x^1+4*x^-1+7*x^0 = 0

(1/2*x^2+7*x^1+4*x^0)/(x^1) = 0 // * x^2

x^1*(1/2*x^2+7*x^1+4*x^0) = 0

x^1

(1/2)*x^2+7*x+4 = 0

(1/2)*x^2+7*x+4 = 0

DELTA = 7^2-(4*4*(1/2))

DELTA = 41

DELTA > 0

x = (41^(1/2)-7)/(2*(1/2)) or x = (-41^(1/2)-7)/(2*(1/2))

x = 41^(1/2)-7 or x = -(41^(1/2)+7)

x in { -(41^(1/2)+7), 41^(1/2)-7} 

x in { -(41^(1/2)+7), 41^(1/2)-7 }

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