Quadratic equations are equations of the form $$ax^2 + bx + c = 0$$, where a, b, and c are constants, and x is the variable. There are several methods for solving quadratic equations, but the most common ones are:

1. Factoring method: If possible, you can factor the quadratic expression into two linear factors, and then set each factor equal to zero to solve for x. For example, the equation $$x^2 + 5x + 6 = 0 $$can be factored as (x+2)(x+3) = 0. Setting each factor equal to zero, you get x=-2 and x=-3 as solutions.

2. Quadratic formula: If the quadratic expression cannot be factored, you can use the quadratic formula: $$ x = (-b ± \sqrt(b^2 – 4ac)) / 2a$$ For example, the equation $$ 2x^2 + 5x – 3 = 0$$ has solutions $$ x = (-5 ± sqrt(5^2 – 4(2)(-3))) / (2(2))$$ Simplifying the expression gives $$ x = (-5 ± sqrt(49)) / 4$$, which is x = (-5 ± 7) / 4. Therefore, the solutions are $$ x = -3/2 and x = 1$$

3. Completing the square: Another method for solving quadratic equations is completing the square, which involves rewriting the quadratic expression in the form (x + p)^2 + q, where p and q are constants. Then, you can solve for x by taking the square root of both sides of the equation. This method is less commonly used than factoring or the quadratic formula, but can be useful in certain situations.

Regardless of which method you choose, always check your solutions by plugging them back into the original equation to make sure they satisfy the equation.