1/3-19/(4x)=1/4-1/6x

Solution for 1/3-19/(4x)=1/4-1/6x equation:

D( x )

4*x = 0

4*x = 0

4*x = 0

4*x = 0 // : 4

x = 0

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

1/3-(19/(4*x)) = 1/4-((1/6)*x) // - 1/4-((1/6)*x)

(1/6)*x-(19/(4*x))+1/3-(1/4) = 0

(1/6)*x+(-19/4)*x^-1+1/3-1/4 = 0

1/6*x^1-19/4*x^-1+1/12*x^0 = 0

(1/6*x^2+1/12*x^1-19/4*x^0)/(x^1) = 0 // * x^2

x^1*(1/6*x^2+1/12*x^1-19/4*x^0) = 0

x^1

(1/6)*x^2+(1/12)*x-19/4 = 0

(1/6)*x^2+(1/12)*x-19/4 = 0

DELTA = (1/12)^2-(4*(1/6)*(-19/4))

DELTA = 457/144

DELTA > 0

x = ((457/144)^(1/2)-(1/12))/(2*(1/6)) or x = (-(1/12)-(457/144)^(1/2))/(2*(1/6))

x = 3*((457/144)^(1/2)-1/12) or x = -3*((457/144)^(1/2)+1/12)

x in { -3*((457/144)^(1/2)+1/12), 3*((457/144)^(1/2)-1/12)} 

x in { -3*((457/144)^(1/2)+1/12), 3*((457/144)^(1/2)-1/12) }