reserve a, a9, a1, a2, a3, b, b9, c, c9, d, d9, h, p, q, x, x1, x2, x3, u, v,
  y, z for Real;

theorem
  b <> 0 & delta(b,c,d) > 0 & Polynom(0,b,c,d,x) = 0 implies x = (-c+
  sqrt delta(b,c,d))/(2*b) or x = (-c-sqrt delta(b,c,d))/(2*b)
proof
  assume
A1: b <> 0 & delta(b,c,d)>0;
  assume Polynom(0,b,c,d,x) = 0;
  then Polynom(b,c,d,x) = 0;
  hence thesis by A1,Th5;
end;
