Urgent help with 2nd Legal Charge needed!

[Frustrated007]

Hi, When my ex-partner sold her property and moved into mine she put up a lump sum towards the mortgage. She wanted some security for the lump sum and also the likley increase in the property value in the future as she would be paying some of my mortgage.

I elected to lodge a charge on the property with the land registry which stated:-

1) On the sale of the property she would receive her lump sum back
2) If the property sold for more than £xxx (The current property value at the time) she would receive an additional 50% of the EQUITY above £xxx.

After I put the property charge on I obtained planning permission to convert the house into four properties which increased its value by £50,000.

There is no loan agreement between myself and ex-partner therefore she can never force a sale or indeed she will never receive any money unless the property is sold.

I have now split with my partner and have started the conversion project, I have a buyer for the four properties once converted and have agreed a price.

I have now offerred my ex-partner a cash lump sum of the amount the house was worth prior to conversion but she won't accept it and wants her share of the properties once developed even though she is not putting any money towards it.

My questions are:-

1) Can I sell the property for what I like?
2) What does the term "EQUITY" actually mean? I presume that I can deduct all conversion costs for the project before she would get her split?
3) The legal charge was done by myself with no solicitors involved (Stupid now I know) can I get out of the charge anyway?

My intention was that she would receive her initial money back and receive a share of the equity above the original property valuation

Please help