5/2x=4/x+9

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Solution for 5/2x=4/x+9 equation: 


D( x )

x = 0

x = 0

x = 0

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

(5/2)*x = 4/x+9 // - 4/x+9

(5/2)*x-(4/x)-9 = 0

(5/2)*x-4*x^-1-9 = 0

5/2*x^1-4*x^-1-9*x^0 = 0

(5/2*x^2-9*x^1-4*x^0)/(x^1) = 0 // * x^2

x^1*(5/2*x^2-9*x^1-4*x^0) = 0

x^1

(5/2)*x^2-9*x-4 = 0

(5/2)*x^2-9*x-4 = 0

DELTA = (-9)^2-(-4*4*(5/2))

DELTA = 121

DELTA > 0

x = (121^(1/2)+9)/(2*(5/2)) or x = (9-121^(1/2))/(2*(5/2))

x = 4 or x = -2/5

x in { -2/5, 4} 

x in { -2/5, 4 }

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