The term “algebra” for one of the branches of mathematics is connected to the title of a work written by the Persian mathematician Muhammad ibn Musa al-Khwarizmi. The title of his work, Al Kitab al-muhtasar fi hisab al-gabr wa-al-muqabala (“A Concise Book on Calculation by Completion and Balancing”), gave rise, through a corruption of the word al-gabr, to the term we use today. This chapter explores the ingenious methods for solving quadratic equations.