(5/x)-(2/3)=(14/3x)

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Solution for (5/x)-(2/3)=(14/3x) equation: 


D( x )

x = 0

x = 0

x = 0

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

5/x-(2/3) = (14/3)*x // - (14/3)*x

5/x-((14/3)*x)-(2/3) = 0

(-14/3)*x+5/x-2/3 = 0

5*x^-1-14/3*x^1-2/3*x^0 = 0

(5*x^0-14/3*x^2-2/3*x^1)/(x^1) = 0 // * x^2

x^1*(5*x^0-14/3*x^2-2/3*x^1) = 0

x^1

(-14/3)*x^2+(-2/3)*x+5 = 0

(-14/3)*x^2+(-2/3)*x+5 = 0

DELTA = (-2/3)^2-(4*5*(-14/3))

DELTA = 844/9

DELTA > 0

x = ((844/9)^(1/2)-(-2/3))/(2*(-14/3)) or x = (-(-2/3)-(844/9)^(1/2))/(2*(-14/3))

x = -3/28*((844/9)^(1/2)+2/3) or x = -3/28*(2/3-(844/9)^(1/2))

x in { -3/28*((844/9)^(1/2)+2/3), -3/28*(2/3-(844/9)^(1/2))} 

x in { -3/28*((844/9)^(1/2)+2/3), -3/28*(2/3-(844/9)^(1/2)) }

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