However, the discriminant would be used prior to solving for the solutions or it can be used after solving for the solutions as a confirmation that you have the correct amount of solutions. Which do you think you would prefer to use the discriminant; i.e.
before solving for the solutions or afterwards?

Before solving for the solutions you should use it to check whether the equation has real roots(if it has solution, you don't write the process on the paper). Afterwards you can use it to check whether you got correct solutions. Sometimes, the equation
can not be decomposed, so you have to use the discriminant to compute the solutions.