(1/x)=(x/6)-(5/60)

Solution for (1/x)=(x/6)-(5/60) equation:

D( x )

x = 0

x = 0

x = 0

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

1/x = x/6-(5/60) // - x/6-(5/60)

1/x-(x/6)+5/60 = 0

1*x^-1-1/6*x^1+1/12*x^0 = 0

(1/12*x^1-1/6*x^2+1*x^0)/(x^1) = 0 // * x^2

x^1*(1/12*x^1-1/6*x^2+1*x^0) = 0

x^1

(-1/6)*x^2+(1/12)*x+1 = 0

(-1/6)*x^2+(1/12)*x+1 = 0

DELTA = (1/12)^2-(1*4*(-1/6))

DELTA = 97/144

DELTA > 0

x = ((97/144)^(1/2)-(1/12))/(2*(-1/6)) or x = (-(1/12)-(97/144)^(1/2))/(2*(-1/6))

x = -3*((97/144)^(1/2)-1/12) or x = 3*((97/144)^(1/2)+1/12)

x in { -3*((97/144)^(1/2)-1/12), 3*((97/144)^(1/2)+1/12)} 

x in { -3*((97/144)^(1/2)-1/12), 3*((97/144)^(1/2)+1/12) }