People's only choice was to petition to the King. Later on the system was changed and then the people's petitions were sent to the Lord Chancellor to deal with.  
Soon enough the law of equity and the common law started to conflict. The fictional case of Jarndyce and Jarndyce in Bleak House written by Charles Dickens is one classic example of such a case. Litigants would go 'jurisdiction shopping' and often would seek an equitable injunction prohibiting the enforcement of a common law court order. The penalty for disobeying an equitable 'common injunction' and enforcing a common law judgment was imprisonment.  
The resolution of the conflict came in the Earl of Oxford's case in 1615 where a judgment of Coke CJ was allegedly obtained by fraud. The Lord Chancellor had issued a common injunction out of the Chancery prohibiting the enforcement of the common law order locking the two courts in a stalemate. Attorney-General at that time, Sir Francis Bacon, upheld the use of the common injunction and concluded that in the event of any conflict between the common law and the equity, equity would prevail. Thus the people's petitions were started to be dealt justly. ...
Generally Equity means fairness. But according to the English law it refers to the body of rules originally enforced only by the Court of the Chancery. It is referred to as a supplement to the common law since it fills in the gaps and makes the English legal system more complete. According to the Farlex Encyclopedia it is defined as a "System of law supplementing the ordinary rules of law where the application of these would operate harshly in a particular case". Sometimes it is regarded as an attempt to achieve 'natural justice'. 
Equity created new rights and as a result of it new procedures were introduced such as the right to subpoena and discovery of documents. The rich nobles resented equity because of the reduction in their incomes. There were advantages that came with it, though, because it was less rigid and formal than the common law resulting in more flexibility. It was a fairer system because it dealt with cases on their merit. A defect was that it lacked certainty and varied from chancellor to chancellor and because overburdened and slow moving. 
Differences with Common Law
England was working with the equity law court and the common law court as described above. The Common Law Courts could only award monetary rewards and damages and it only recognized the legal owner of property. On the other hand the Equity Law Courts could issue injunctive relief and recognized trusts of property. This distinction between common law and equity was categorized and prioritized the rights to property. It further helped in determining whether the Seventh Amendment's right to a jury trial applies or whether the issue may be decided by a