6/x=10/9x+1

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Solution for 6/x=10/9x+1 equation: 


D( x )

x = 0

x = 0

x = 0

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

6/x = (10/9)*x+1 // - (10/9)*x+1

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

(-10/9)*x+6/x-1 = 0

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

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

x^1*(6*x^0-10/9*x^2-1*x^1) = 0

x^1

(-10/9)*x^2-x+6 = 0

(-10/9)*x^2-x+6 = 0

DELTA = (-1)^2-(4*6*(-10/9))

DELTA = 83/3

DELTA > 0

x = ((83/3)^(1/2)+1)/(2*(-10/9)) or x = (1-(83/3)^(1/2))/(2*(-10/9))

x = -9/20*((83/3)^(1/2)+1) or x = -9/20*(1-(83/3)^(1/2))

x in { -9/20*((83/3)^(1/2)+1), -9/20*(1-(83/3)^(1/2))} 

x in { -9/20*((83/3)^(1/2)+1), -9/20*(1-(83/3)^(1/2)) }

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