A quadratic equation is a second degree (order) polynomial equation, thus it is guaranteed to have two solutions, both of which may be real or complex. This is seen in the standard form ax² + bx + c = 0.

The roots of x can be found in the equation by factoring and completing the square (a method of transforming a quadratic equation so that it is in the form of a perfect square). For example, to solve the equation x² - 3x = 4 by factoring, you would do the following:

First, write the equation in standard quadratic equation form:

Then factor the form:

In order for these numbers to equal zero, we determine that for (x - 4), x would be 4; and for (x + 1), x would equal -1. Thus, the solutions are 4 and -1.