3/x-1=8/3x

Solution for 3/x-1=8/3x equation:

D( x )

x = 0

x = 0

x = 0

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

3/x-1 = (8/3)*x // - (8/3)*x

3/x-((8/3)*x)-1 = 0

(-8/3)*x+3/x-1 = 0

3*x^-1-8/3*x^1-1*x^0 = 0

(3*x^0-8/3*x^2-1*x^1)/(x^1) = 0 // * x^2

x^1*(3*x^0-8/3*x^2-1*x^1) = 0

x^1

(-8/3)*x^2-x+3 = 0

(-8/3)*x^2-x+3 = 0

DELTA = (-1)^2-(3*4*(-8/3))

DELTA = 33

DELTA > 0

x = (33^(1/2)+1)/(2*(-8/3)) or x = (1-33^(1/2))/(2*(-8/3))

x = -3/16*(33^(1/2)+1) or x = -3/16*(1-33^(1/2))

x in { -3/16*(33^(1/2)+1), -3/16*(1-33^(1/2))} 

x in { -3/16*(33^(1/2)+1), -3/16*(1-33^(1/2)) }