5/2x-7=3/x-3

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

5/2*x^1-3*x^-1-4*x^0 = 0

(5/2*x^2-4*x^1-3*x^0)/(x^1) = 0 // * x^2

x^1*(5/2*x^2-4*x^1-3*x^0) = 0

x^1

(5/2)*x^2-4*x-3 = 0

(5/2)*x^2-4*x-3 = 0

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

DELTA = 46

DELTA > 0

x = (46^(1/2)+4)/(2*(5/2)) or x = (4-46^(1/2))/(2*(5/2))

x = (46^(1/2)+4)/5 or x = (4-46^(1/2))/5

x in { (4-46^(1/2))/5, (46^(1/2)+4)/5} 

x in { (4-46^(1/2))/5, (46^(1/2)+4)/5 }

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