Hello,
After a night,
f(x,y)=0 ==>df=0==>@f/@x*dx+@f/@y*dy=0
==>dy/dx=-(@f/@x)/(@f/@y) There was a mistake (in my memory)
@f/@x=6xy²+20x^4
@f/@y=5y^4+6x²y
==>dy/dx=-(6xy²+20x^3)/(5y^4+6x²y)
for x=-1 and y=2 dy/dx= -(6*(-1)*4+20*(-1)^3)/(5*2^4+6*(-1)²*2)
=44/92=11/23
or
5y^4*dy/dx+6xy²+6x²ydy/dx+20x^3=0
==>dy/dx*(5y^4+6x²y)=-6xy²-20x^3
==>dy/dx= -(6xy²+20x^3)/(5y^4+6x²y)
==>11/23