reserve k,m,n,p for Nat;
reserve x, a, b, c for Real;

theorem Th6:
  for x, a, b, c being Real st a <> 0 & delta(a,b,c) >= 0
holds a * x^2 + b * x + c = 0 iff (x = (- b - sqrt delta(a,b,c))/(2 * a) or x =
  (- b + sqrt delta(a,b,c))/(2 * a))
proof
  let x, a, b, c;
  set lh = a * x^2 + b * x + c;
  set r1 = (- b - sqrt delta(a,b,c))/(2 * a);
  set r2 = ( - b + sqrt delta(a,b,c))/(2 * a);
  assume that
A1: a <> 0 and
A2: delta(a,b,c) >= 0;
  lh = a * (x - r1) * (x - r2) by A1,A2,QUIN_1:16;
  hence thesis by A1,A2,QUIN_1:15;
end;
