5/2x-3/10=1/x

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Solution for 5/2x-3/10=1/x equation: 


D( x )

x = 0

x = 0

x = 0

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

(5/2)*x-(3/10) = 1/x // - 1/x

(5/2)*x-(1/x)-(3/10) = 0

(5/2)*x-x^-1-3/10 = 0

5/2*x^1-1*x^-1-3/10*x^0 = 0

(5/2*x^2-3/10*x^1-1*x^0)/(x^1) = 0 // * x^2

x^1*(5/2*x^2-3/10*x^1-1*x^0) = 0

x^1

(5/2)*x^2+(-3/10)*x-1 = 0

(5/2)*x^2+(-3/10)*x-1 = 0

DELTA = (-3/10)^2-(-1*4*(5/2))

DELTA = 1009/100

DELTA > 0

x = ((1009/100)^(1/2)-(-3/10))/(2*(5/2)) or x = (-(-3/10)-(1009/100)^(1/2))/(2*(5/2))

x = ((1009/100)^(1/2)+3/10)/5 or x = (3/10-(1009/100)^(1/2))/5

x in { (3/10-(1009/100)^(1/2))/5, ((1009/100)^(1/2)+3/10)/5} 

x in { (3/10-(1009/100)^(1/2))/5, ((1009/100)^(1/2)+3/10)/5 }

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