1/2x-5/16=1/x

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Solution for 1/2x-5/16=1/x equation: 


D( x )

x = 0

x = 0

x = 0

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

(1/2)*x-(5/16) = 1/x // - 1/x

(1/2)*x-(1/x)-(5/16) = 0

(1/2)*x-x^-1-5/16 = 0

1/2*x^1-1*x^-1-5/16*x^0 = 0

(1/2*x^2-5/16*x^1-1*x^0)/(x^1) = 0 // * x^2

x^1*(1/2*x^2-5/16*x^1-1*x^0) = 0

x^1

(1/2)*x^2+(-5/16)*x-1 = 0

(1/2)*x^2+(-5/16)*x-1 = 0

DELTA = (-5/16)^2-(-1*4*(1/2))

DELTA = 537/256

DELTA > 0

x = ((537/256)^(1/2)-(-5/16))/(2*(1/2)) or x = (-(-5/16)-(537/256)^(1/2))/(2*(1/2))

x = (537/256)^(1/2)+5/16 or x = 5/16-(537/256)^(1/2)

x in { 5/16-(537/256)^(1/2), (537/256)^(1/2)+5/16} 

x in { 5/16-(537/256)^(1/2), (537/256)^(1/2)+5/16 }

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