1/x-10/3x=1/9

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Solution for 1/x-10/3x=1/9 equation:


D( x )

x = 0

x = 0

x = 0

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

1/x-((10/3)*x) = 1/9 // - 1/9

1/x-((10/3)*x)-(1/9) = 0

(-10/3)*x+1/x-1/9 = 0

1*x^-1-10/3*x^1-1/9*x^0 = 0

(1*x^0-10/3*x^2-1/9*x^1)/(x^1) = 0 // * x^2

x^1*(1*x^0-10/3*x^2-1/9*x^1) = 0

x^1

(-10/3)*x^2+(-1/9)*x+1 = 0

(-10/3)*x^2+(-1/9)*x+1 = 0

DELTA = (-1/9)^2-(1*4*(-10/3))

DELTA = 1081/81

DELTA > 0

x = ((1081/81)^(1/2)-(-1/9))/(2*(-10/3)) or x = (-(-1/9)-(1081/81)^(1/2))/(2*(-10/3))

x = -3/20*((1081/81)^(1/2)+1/9) or x = -3/20*(1/9-(1081/81)^(1/2))

x in { -3/20*((1081/81)^(1/2)+1/9), -3/20*(1/9-(1081/81)^(1/2))}

x in { -3/20*((1081/81)^(1/2)+1/9), -3/20*(1/9-(1081/81)^(1/2)) }

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