of ax^2+bx+c=0
in Ax+B=0
A^2c-ABb+B^2a
in Ax^2+Bx+C=0
A^2c^2+A(Cb^2-Bbc-2Cac)
+C^2a^2-BCab+B^2ac
in Ax^3+Bx^2+Cx+D=0
A^2c^3+A(-2Cac^2+3Dabc-Bbc^2+Cb^2c-Db^3)
+D^2a^3+C^2a^2c-2BDa^2c-CDa^2b-BCabc+B^2ac^2+BDab^2
in Ax^4+Bx^3+Cx^2+Dx+F=0
A^2c^4+A(2Fa^2c^2+3Dabc^2-4Fab^2c-2Cac^3-Db^3c-Bbc^3+Fb^4+Cb^2c^2)
+F^2a^4+D^2a^3c-2CFa^3c-DFa^3b-CDa^2bc-2BDa^2c^2+3BFa^2bc+C^2a^2c^2+CFa^2b^2-BCabc^2+BDab^2c+B^2ac^3-BFab^3
in Ax^5+Bx^4+Cx^3+Dx^2+Fx+G=0
A^2c^5+A(2Fa^2c^3-5Ga^2bc^2+3Dabc^3-4Fab^2c^2-2Cac^4+5Gab^3c+Fb^4c+Cb^2c^3-Db^3c^2-Bbc^4-Gb^5)
+G^2a^5+F^2a^4c-2DGa^4c-FGa^4b-DFa^3bc-2CFa^3c^2+3CGa^3bc+D^2a^3c^2+DGa^3b^2+2BGa^3c^2-CDa^2bc^2+3BFa^2bc^2+CFa^2b^2c+C^2a^2c^3-4BGa^2b^2c-CGa^2b^3-2BDa^2c^3-BFab^3c-BCabc^3+BGab^4+BDab^2c^2+B^2ac^4
in Ax^6+Bx^5+Cx^4+Dx^3+Fx^2+Gx+H=0
A^2c^6+A(-Bbc^5-2Cac^5+Cb^2c^4+3Dabc^4-Db^3c^3+2Fa^2c^4-4Fab^2c^3+Fb^4c^2-5Ga^2bc^3+5Gab^3c^2-Gb^5c-2Ha^3c^3+9Ha^2b^2c^2-6Hab^4c+Hb^6)
+H^2a^6+G^2a^5c-2FHa^5c-GHa^5b-FGa^4bc-2DGa^4c^2+3DHa^4bc+F^2a^4c^2+FHa^4b^2-DFa^3bc^2+DGa^3b^2c+D^2a^3c^3-DHa^3b^3+C^2a^2c^4-CDa^2bc^3+CFa^2b^2c^2-2CFa^3c^3-CGa^2b^3c+3CGa^3bc^2+2CHa^4c^2-4CHa^3b^2c+CHa^2b^4+B^2ac^5-BCabc^4-2BDa^2c^4+BDab^2c^3+3BFa^2bc^3-BFab^3c^2+2BGa^3c^3-4BGa^2b^2c^2+BGab^4c+5BHa^2b^3c-BHab^5-5BHa^3bc^2
in Ax^7+Bx^6+Cx^5+Dx^4+Fx^3+Gx^2+Hx+J=0
A^2c^7+A(-2Ha^3c^4+7a^3bc^3J-5Ga^2bc^4+9Ha^2b^2c^3+2Fa^2c^5-14a^2b^3c^2J-4Fab^2c^4+5Gab^3c^3-6Hab^4c^2+3Dabc^5-2Cac^6+7ab^5cJ+Hb^6c-Db^3c^4+Fb^4c^3-Gb^5c^2+Cb^2c^5-Bbc^6-b^7J)
+a^7J^2+H^2a^6c-2Ga^6cJ-Ha^6bJ-GHa^5bc-2FHa^5c^2+3Fa^5bcJ+G^2a^5c^2+Ga^5b^2J+2Da^5c^2J-FGa^4bc^2+3DHa^4bc^2+FHa^4b^2c+2CHa^4c^3+F^2a^4c^3-4Da^4b^2cJ-Fa^4b^3J-2DGa^4c^3-5Ca^4bc^2J-2Ba^4c^3J-DHa^3b^3c+3CGa^3bc^3-4CHa^3b^2c^2-5BHa^3bc^3-DFa^3bc^3-2CFa^3c^4+5Ca^3b^3cJ+Da^3b^4J+DGa^3b^2c^2+2BGa^3c^4+9Ba^3b^2c^2J+D^2a^3c^4+CHa^2b^4c+CFa^2b^2c^3-CGa^2b^3c^2-4BGa^2b^2c^3+5BHa^2b^3c^2-CDa^2bc^4+3BFa^2bc^4+C^2a^2c^5-6Ba^2b^4cJ-Ca^2b^5J-2BDa^2c^5-BHab^5c-BFab^3c^3+BGab^4c^2+BDab^2c^4-BCabc^5+Bab^6J+B^2ac^6
2in2
(Ac-Ca)^2=-B^2ac+Bb(Ac+Ca)-ACb^2
2in4
(Ac^2+Fa^2)^2+C^2a^2c^2-Cac(2Fa^2+2Ac^2+Dab+Bbc)+Cb^2(+Ac^2+Fa^2)-4AFab^2c+AFb^4-DFa^3b+3BFa^2bc-BFab^3+3ADabc^2-ADb^3c-ABbc^3+D^2a^3c-2BDa^2c^2+BDab^2c+B^2ac^3