Book Maths Puzzle Profit and Loss

Is there a way to explain the Quadratic Formula in laymans terms??? I am going to teach Elem. Ed, and is there a simpler way to explain it to my students??? Also, is there any proofs for why factoring works?? I've searched and searched, and I cannot find any proofs.

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Book Other Question

How do you graph this....
y= -7x + 14
3x^2 - 9x + 5 < 0
It has been years since I have had an algebra class. I cannot remember how to solve this problem. Thank You!