5-(1/x)=10/3x

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Solution for 5-(1/x)=10/3x equation:


D( x )

x = 0

x = 0

x = 0

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

5-(1/x) = (10/3)*x // - (10/3)*x

5-((10/3)*x)-(1/x) = 0

(-10/3)*x-x^-1+5 = 0

5*x^0-10/3*x^1-1*x^-1 = 0

(5*x^1-10/3*x^2-1*x^0)/(x^1) = 0 // * x^2

x^1*(5*x^1-10/3*x^2-1*x^0) = 0

x^1

(-10/3)*x^2+5*x-1 = 0

(-10/3)*x^2+5*x-1 = 0

DELTA = 5^2-(-1*4*(-10/3))

DELTA = 35/3

DELTA > 0

x = ((35/3)^(1/2)-5)/(2*(-10/3)) or x = (-(35/3)^(1/2)-5)/(2*(-10/3))

x = -3/20*((35/3)^(1/2)-5) or x = 3/20*((35/3)^(1/2)+5)

x in { -3/20*((35/3)^(1/2)-5), 3/20*((35/3)^(1/2)+5)}

x in { -3/20*((35/3)^(1/2)-5), 3/20*((35/3)^(1/2)+5) }

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