When solving quadratic equations, we can use two main methods: factoring and the quadratic formula. Each method has its own advantages.

Factoring:

• This method works well when we can easily break down the equation into simpler parts.
• For example, with the equation (x^2 - 5x + 6 = 0), we can factor it to ((x - 2)(x - 3) = 0).
• This gives us the answers, or roots, of (x = 2) and (x = 3).

Quadratic Formula:

• This method is helpful when factoring is too hard or doesn’t work at all.
• The formula looks like this: (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}).
• For example, in the equation (2x^2 - 4x - 6 = 0), we can use the quadratic formula to find the roots. Here, we find (x = 3) and (x = -1).

In short, use factoring for easier quadratic equations and the quadratic formula for the tougher ones!