Firstly, the title may be a little hard to understand so could someone please suggest a better one and make up for my 'ignorance.'
Onto the question. If I have a quadratic equation: $$ax^2+bx+c$$ Is there a way for me to factor this to $(nx+r)(tx+s)$ by just using an equation. For example say I have the equation: $$2x^2+x-6$$ Can I factor this to $(2x-3)(x+2)$ only using an equation not the traditional method of look, guess, test : if right stop, if wrong repeat.
The reason I ask this is because I have made a formula to do what I have described and I am not sure if any mathematicians have done this before. I want to know if I have made a discovery or rediscovered something already found.
The formula is $d$ = quadratic formula, $ax^2+bx+c = (x-d)*(x -(ad+b))$