Artificial intelligence (AI) is transforming decision-making processes in finance, notably in credit scoring, where machine learning (ML) models enhance predictive accuracy. However, these models often rely on historical data containing biases, leading to unfair treatment of certain demographic groups based on race or gender. This paper presents two optimisation-based methods to enforce fairness in ML for credit scoring. The first approach uses constraint-based optimisation to reduce bias by regularising the decision boundary, while the second employs adversarial learning to equalise score distributions across demographic groups. Applied to real-world datasets, these methods achieve demographic parity, upholding fairness without significantly sacrificing predictive performance. The findings suggest that integrating fairness constraints into AI models can help finance applications mitigate discrimination, leading to more equitable outcomes in credit scoring.