(2/3x)-6=(5/x)

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Solution for (2/3x)-6=(5/x) equation:


D( x )

x = 0

x = 0

x = 0

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

(2/3)*x-6 = 5/x // - 5/x

(2/3)*x-(5/x)-6 = 0

(2/3)*x-5*x^-1-6 = 0

2/3*x^1-5*x^-1-6*x^0 = 0

(2/3*x^2-6*x^1-5*x^0)/(x^1) = 0 // * x^2

x^1*(2/3*x^2-6*x^1-5*x^0) = 0

x^1

(2/3)*x^2-6*x-5 = 0

(2/3)*x^2-6*x-5 = 0

DELTA = (-6)^2-(-5*4*(2/3))

DELTA = 148/3

DELTA > 0

x = ((148/3)^(1/2)+6)/(2*(2/3)) or x = (6-(148/3)^(1/2))/(2*(2/3))

x = 3/4*((148/3)^(1/2)+6) or x = 3/4*(6-(148/3)^(1/2))

x in { 3/4*(6-(148/3)^(1/2)), 3/4*((148/3)^(1/2)+6)}

x in { 3/4*(6-(148/3)^(1/2)), 3/4*((148/3)^(1/2)+6) }

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