(3/2x)-(7/x-5)=1/x

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Solution for (3/2x)-(7/x-5)=1/x equation: 


D( x )

x = 0

x = 0

x = 0

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

(3/2)*x-(7/x)+5 = 1/x // - 1/x

(3/2)*x-(7/x)-(1/x)+5 = 0

(3/2)*x-7*x^-1-x^-1+5 = 0

3/2*x^1-8*x^-1+5*x^0 = 0

(3/2*x^2+5*x^1-8*x^0)/(x^1) = 0 // * x^2

x^1*(3/2*x^2+5*x^1-8*x^0) = 0

x^1

(3/2)*x^2+5*x-8 = 0

(3/2)*x^2+5*x-8 = 0

DELTA = 5^2-(-8*4*(3/2))

DELTA = 73

DELTA > 0

x = (73^(1/2)-5)/(2*(3/2)) or x = (-73^(1/2)-5)/(2*(3/2))

x = (73^(1/2)-5)/3 or x = (-(73^(1/2)+5))/3

x in { (-(73^(1/2)+5))/3, (73^(1/2)-5)/3} 

x in { (-(73^(1/2)+5))/3, (73^(1/2)-5)/3 }

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