And the tests are straightforward and fast compute

discriminant = (float)Math.Sqrt((double)discriminant);

float s0 = (-b + discriminant) / 2.0F;
float s1 = (-b - discriminant) / 2.0F;

The picking ray extends infinitely, so there is a possibility that multiple objects can be intersected. The object closest to the camera is the one the user selected because it will always occlude the other selected objects.

Improving Intersection Accuracy

private bool IntersectRayMesh(Entity entity, int x, int y) {
PickingRay ray = ComputePickingRay(entity, x, y);
return entity.Mesh.Intersect(ray.Origin, ray.Direction); }

Using Built-In D3DX Functionality

near = new Vector3(x, y, 0);
far = new Vector3(x, y, 1);

Matrix world = Matrix.Identity;
world.Translate(entity.Position);