2x-7/x=x-5/2

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Solution for 2x-7/x=x-5/2 equation: 


D( x )

x = 0

x = 0

x = 0

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

2*x-(7/x) = x-(5/2) // - x-(5/2)

2*x-x-(7/x)+5/2 = 0

2*x-x-7*x^-1+5/2 = 0

1*x^1-7*x^-1+5/2*x^0 = 0

(1*x^2+5/2*x^1-7*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^2+5/2*x^1-7*x^0) = 0

x^1

x^2+(5/2)*x-7 = 0

x^2+(5/2)*x-7 = 0

DELTA = (5/2)^2-(-7*1*4)

DELTA = 137/4

DELTA > 0

x = ((137/4)^(1/2)-(5/2))/(1*2) or x = (-(5/2)-(137/4)^(1/2))/(1*2)

x = ((137/4)^(1/2)-5/2)/2 or x = (-((137/4)^(1/2)+5/2))/2

x in { (-((137/4)^(1/2)+5/2))/2, ((137/4)^(1/2)-5/2)/2} 

x in { (-((137/4)^(1/2)+5/2))/2, ((137/4)^(1/2)-5/2)/2 }

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