x/3-5/x=7/2

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

DELTA = (-7/2)^2-(-5*4*(1/3))

DELTA = 227/12

DELTA > 0

x = ((227/12)^(1/2)-(-7/2))/(2*(1/3)) or x = (-(-7/2)-(227/12)^(1/2))/(2*(1/3))

x = 3/2*((227/12)^(1/2)+7/2) or x = 3/2*(7/2-(227/12)^(1/2))

x in { 3/2*(7/2-(227/12)^(1/2)), 3/2*((227/12)^(1/2)+7/2)} 

x in { 3/2*(7/2-(227/12)^(1/2)), 3/2*((227/12)^(1/2)+7/2) }

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