2x+1=5/x+2

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Solution for 2x+1=5/x+2 equation: 


D( x )

x = 0

x = 0

x = 0

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

2*x+1 = 5/x+2 // - 5/x+2

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

2*x-5*x^-1-2+1 = 0

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

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

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

x^1

2*x^2-x-5 = 0

2*x^2-x-5 = 0

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

DELTA = 41

DELTA > 0

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

x = (41^(1/2)+1)/4 or x = (1-41^(1/2))/4

x in { (1-41^(1/2))/4, (41^(1/2)+1)/4} 

x in { (1-41^(1/2))/4, (41^(1/2)+1)/4 }

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