8-1/x=1/9x

Solution for 8-1/x=1/9x equation:

D( x )

x = 0

x = 0

x = 0

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

8-(1/x) = (1/9)*x // - (1/9)*x

8-((1/9)*x)-(1/x) = 0

(-1/9)*x-x^-1+8 = 0

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

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

x^1*(8*x^1-1/9*x^2-1*x^0) = 0

x^1

(-1/9)*x^2+8*x-1 = 0

(-1/9)*x^2+8*x-1 = 0

DELTA = 8^2-(-1*4*(-1/9))

DELTA = 572/9

DELTA > 0

x = ((572/9)^(1/2)-8)/(2*(-1/9)) or x = (-(572/9)^(1/2)-8)/(2*(-1/9))

x = -9/2*((572/9)^(1/2)-8) or x = 9/2*((572/9)^(1/2)+8)

x in { -9/2*((572/9)^(1/2)-8), 9/2*((572/9)^(1/2)+8)} 

x in { -9/2*((572/9)^(1/2)-8), 9/2*((572/9)^(1/2)+8) }