diff --git a/aoc/day06.py b/aoc/day06.py
index 091844f..9fa4fd7 100644
--- a/aoc/day06.py
+++ b/aoc/day06.py
@@ -1,5 +1,6 @@
 from dataclasses import dataclass
 from functools import reduce
+from math import ceil, floor, sqrt
 
 import re
 
@@ -13,9 +14,10 @@ class Race:
 
 
 class Day06(AocSameImplementation[list[Race]], Aoc2[list[Race], list[Race]]):
-    def simulate(self, timeaccel: int, timeoverall: int) -> int:
-        racetime = timeoverall - timeaccel
-        return racetime * timeaccel
+    def is_zero(self, to: int, d: int) -> tuple[int, int]:
+        return floor(to / 2 - sqrt((-to / 2) ** 2 - d) + 1), ceil(
+            to / 2 + sqrt((-to / 2) ** 2 - d) - 1
+        )
 
     def parseinput2(self, inpt: str) -> list[Race]:
         lines = inpt.splitlines()
@@ -34,16 +36,7 @@ class Day06(AocSameImplementation[list[Race]], Aoc2[list[Race], list[Race]]):
     def part(self, inpt: list[Race]) -> int:
         return reduce(
             lambda x, y: x * y,
-            [
-                len(
-                    [
-                        poss
-                        for poss in range(race.time)
-                        if self.simulate(poss, race.time) > race.distance
-                    ]
-                )
-                for race in inpt
-            ],
+            (e - s + 1 for s, e in (self.is_zero(r.time, r.distance) for r in inpt)),
         )