We update the weights by multiplying the learning rate times our gradient, and then adding in momentum and multiplying by the previous delta. This is then run through each input synapse to calculate the final value:

public void UpdateWeights(double learnRate, double momentum)
{
  var prevDelta = BiasDelta;
  BiasDelta = learnRate * Gradient;
  Bias += BiasDelta + momentum * prevDelta;

  foreach (var synapse in InputSynapses)
  {
    prevDelta = synapse.WeightDelta;
    synapse.WeightDelta = learnRate * Gradient * synapse.InputNeuron.Value;
        synapse.Weight += synapse.WeightDelta + momentum * prevDelta;
  }
}