A quadratic equation is an equation that can be put in the form of a second degree polynomial equal to zero. A second-degree polynomial has an x2 term, and possibly an x term, and perhaps a constant term, but no other appearances of the variable. Sometimes terms have to be moved from the side of the equation that will become zero by addition or subtraction. Sometimes symbols of grouping will need to be removed, a process often requiring the distribution of multiplication over addition. The distribution property is a(b + c) = ab + ac. And sometimes like terms, those to with the variable raised to the same power, will need to be combined.
A quadratic equation can have as many as two solutions. Some have only one solution, which is repeated. It is possible the solutions are complex numbers. If they are, the solutions are conjugates of each other, meaning if one is of the form a + bi the other is of the form a – bi.