(1/x-6)=(3/12x)

Solution for (1/x-6)=(3/12x) equation:

D( x )

x = 0

x = 0

x = 0

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

1/x-6 = (3/12)*x // - (3/12)*x

1/x-((3/12)*x)-6 = 0

(-1/4)*x+1/x-6 = 0

1*x^-1-1/4*x^1-6*x^0 = 0

(1*x^0-1/4*x^2-6*x^1)/(x^1) = 0 // * x^2

x^1*(1*x^0-1/4*x^2-6*x^1) = 0

x^1

(-1/4)*x^2-6*x+1 = 0

(-1/4)*x^2-6*x+1 = 0

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

DELTA = 37

DELTA > 0

x = (37^(1/2)+6)/(2*(-1/4)) or x = (6-37^(1/2))/(2*(-1/4))

x = -2*(37^(1/2)+6) or x = -2*(6-37^(1/2))

x in { -2*(37^(1/2)+6), -2*(6-37^(1/2))} 

x in { -2*(37^(1/2)+6), -2*(6-37^(1/2)) }