diff --git a/src/main.rs b/src/main.rs
index fd3e07e..d605127 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -11,15 +11,15 @@ use crate::{
 
 fn hit_sphere(center: &Point3, radius: f64, r: &Ray) -> f64 {
     let oc = r.origin() - *center;
-    let a = r.direction().dot(&r.direction());
-    let b = 2.0 * oc.dot(&r.direction());
-    let c = oc.dot(&oc) - radius*radius;
-    let discriminant = b*b - 4.0*a*c;
+    let a = r.direction().length_squared();
+    let half_b = oc.dot(&r.direction());
+    let c = oc.length_squared() - radius*radius;
+    let discriminant = half_b*half_b - a*c;
 
     if discriminant < 0.0 {
         -1.0
     } else {
-        (-b - discriminant.sqrt()) / (2.0 * a)
+        (-half_b - discriminant.sqrt()) / a
     }
 }