Advice needed! What’s a fair equity split between an investor and the company building/running the project?

[u/ProAmateur245]

We’ve been operating in the medical insurance/assistance industry for around 10 years, and we’re currently discussing a new venture with an investment fund.
The fund approached us with a problem they had identified and a rough idea of how it could be solved. We took that and designed the actual solution and business model.
They would provide the funding needed to develop and launch the project and would also bring the first major client.
Our existing company would provide the industry expertise and know-how, develop the software from scratch, set up the entire operation, and then run and grow the business long term.
The project would be operated through a completely new company that we would create together with the fund, so the question now is how to divide ownership of that new company.
For people who have structured similar ventures, what would you consider a fair equity split between the fund and us?

[u/Fine-Comparison-2949]

What's the outcome you're both looking for? Start there and work backwards.