I’m trying to code my own raytracer for a particle system to draw particles that are a bit overlapped by others with a darker color. Particle is a circle. So I want to trace ray from each particle’s center to a light source. My HLSL:

   Particle particle = sbParticles[index];
   Particle lightSource = sbParticles[2];
   
   float shadowFactor = 1.0f;
   
   float3 rayDirection = normalize(lightSource.pos - particle.pos);
   float3 origin = particle.pos;

   float a = dot(rayDirection, rayDirection);
   float b = 2.0 * dot(rayDirection, origin);
   float c = dot(origin, origin) - particle.radius * particle.radius;
   
   float discriminant = b * b - 4.0 * a * c;

   if (discriminant < 0.0f)
   {
       shadowFactor = 0.0f;
   }
   else
   {
       float t0 = (-b - sqrt(discriminant)) / (2.0 * a);
       float t1 = (-b + sqrt(discriminant)) / (2.0 * a);
       float t = min(t0, t1);
       
       if (t > 0.0f) shadowFactor = 1.0f;
   }

Particles positions:

    sbParticles[0].pos = XMFLOAT3(-100.0, 60.0, 20.0);
    sbParticles[0].radius = 70.0f;

    sbParticles[1].pos = XMFLOAT3(100.0, 60.0, 20.0);
    sbParticles[1].radius = 70.0f;

    sbParticles[2].pos = XMFLOAT3(400.0, 60.0, 20.0); // light source
    sbParticles[2].radius = 70.0f;

But when I run this code it doesn’t work as I expect. As you can see, sbParticles[1] is next to sbParticles[0], so I want to trace a ray from sbParticles[0] and hit sbParticles[1]. Discriminant is positive (it’s always positive, even when sbParticles[1] does not overlap sbParticles[0] at all !). And t contains 70, which is the particle’s radius.
What math am I missing?