9/x=10/9x+1

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

D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

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

DELTA = 41

DELTA > 0

x = (41^(1/2)+1)/(2*(-10/9)) or x = (1-41^(1/2))/(2*(-10/9))

x = -9/20*(41^(1/2)+1) or x = -9/20*(1-41^(1/2))

x in { -9/20*(41^(1/2)+1), -9/20*(1-41^(1/2))} 

x in { -9/20*(41^(1/2)+1), -9/20*(1-41^(1/2)) }