subroutine quartc(a,b,c,x)      
C     ==========================
c    
c     solver for the algebraic equation of the fourth order
c     a*x**4 + b*x =c
c
c     solution done by the Newton-Raphson method
c
c     Initial estimate
c
      INCLUDE 'IMPLIC.FOR'
c
      if(a.gt.b) then
         x=(c/a)**0.25
        else
        x=c/b
      end if
c          
      it=0
   10 continue
      it=it+1
      ax=a*x**3
      v=c-b*x-x*ax
      d=4.*ax+b
      if(d.ne.0.) dx=v/d
      x=x+dx
      if(abs(dx/x).gt.1.e-3) then
         if(it.lt.20) go to 10
       else
         if(it.ge.20) write(6,601) a,b,c,dx,x 
      end if
  601 format(' slow convergence of quartic solver'/
     *       ' a,b,c,dx,x = ',1p5e13.4)
      return
      end