1/x=9/4x+5

Solution for 1/x=9/4x+5 equation:

D( x )

x = 0

x = 0

x = 0

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

1/x = (9/4)*x+5 // - (9/4)*x+5

1/x-((9/4)*x)-5 = 0

(-9/4)*x+1/x-5 = 0

1*x^-1-9/4*x^1-5*x^0 = 0

(1*x^0-9/4*x^2-5*x^1)/(x^1) = 0 // * x^2

x^1*(1*x^0-9/4*x^2-5*x^1) = 0

x^1

(-9/4)*x^2-5*x+1 = 0

(-9/4)*x^2-5*x+1 = 0

DELTA = (-5)^2-(1*4*(-9/4))

DELTA = 34

DELTA > 0

x = (34^(1/2)+5)/(2*(-9/4)) or x = (5-34^(1/2))/(2*(-9/4))

x = -2/9*(34^(1/2)+5) or x = -2/9*(5-34^(1/2))

x in { -2/9*(34^(1/2)+5), -2/9*(5-34^(1/2))} 

x in { -2/9*(34^(1/2)+5), -2/9*(5-34^(1/2)) }