To solve quadratic equations, which are mathematical expressions in the form of ax² + bx + c = 0, where a, b, and c are constants, you can use several methods. The most common methods include factoring, completing the square, and applying the quadratic formula, which is x = (-b ± √(b² - 4ac)) / 2a. Finding the solutions, or roots, of a quadratic equation helps identify the values of x where the equation equals zero. These solutions can be real or complex numbers, depending on the value of the discriminant, b² - 4ac.