Your example makes sense dramatically but the word equity, in my experience is seldom used in this context.
Equity, is very frequently used to discuss the value of shares which are issued by companies, or the proportion of ownership which a person has when they purchase a property using a mortgage.
For example, if a person buys a house which has a value of $100,000 by paying $10,000 and borrowing the other $90,000, that person's equity in the house is only $10,000. It is often said that the owner has a 10% equity in this property because, after paying the debt, his proportion of the ownership is only 10% of the total value.
Equality, on the other hand, refers to a condition of two or more things which have the same value. The mathematical "equals sign (=) denotes, equality on both sides of the equation.