1/x=5/4+x

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Solution for 1/x=5/4+x equation: 


D( x )

x = 0

x = 0

x = 0

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

1/x = x+5/4 // - x+5/4

1/x-x-(5/4) = 0

1/x-x-5/4 = 0

1*x^-1-1*x^1-5/4*x^0 = 0

(1*x^0-1*x^2-5/4*x^1)/(x^1) = 0 // * x^2

x^1*(1*x^0-1*x^2-5/4*x^1) = 0

x^1

(-5/4)*x-x^2+1 = 0

(-5/4)*x-x^2+1 = 0

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

DELTA = 89/16

DELTA > 0

x = ((89/16)^(1/2)-(-5/4))/(-1*2) or x = (-(-5/4)-(89/16)^(1/2))/(-1*2)

x = ((89/16)^(1/2)+5/4)/(-2) or x = (5/4-(89/16)^(1/2))/(-2)

x in { ((89/16)^(1/2)+5/4)/(-2), (5/4-(89/16)^(1/2))/(-2)} 

x in { ((89/16)^(1/2)+5/4)/(-2), (5/4-(89/16)^(1/2))/(-2) }

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