Solving for X In financial world - Playing with formulas

I am looking to create a template to solve for x in financial world. my efforts to do this made me realize that my ambitions are outrunning my capabilities.

Scenario
I want a quick way to work toward a blended rate.
So, if my loan is $950M
and the main facility is $900M at 6.5%
and the blended rate cap is 7%
what rate can the participant portion of $50M be set at?

To figure the blended rate normally, I take the Sum(($*%)+($*%))/Facility amount.

I want to be able to solve for $ or % when needed.
I appreciate any feedback!

You're leaving out details. If there were just one loan repayment exactly 1 year after you took out the full $950M, then

950M * 0.07 = 900M * 0.065 + 50M * r -> r = (950M * 0.07 - 900M * 0.065) / 50M = 0.16, so 16%