The art of understanding (rather than simply solving) quadratics is to factorise them, thus...
2X²-7X-15 = 0
(divide through by 2)
X²-3.5X - 7.5 = 0
This must have a form (X+a)(X+b)=X²+(a+b)X+ab=0
Or in other words, a*b=-7.5, and a+b=-3.5
Play around with numbers a bit, and you'll see that this works for a=-5 and b=1.5, ziv...
(X+1.5)(X-5) = X²-3.5X-7.5 = 0
[or if you prefer, 2(X+1.5)(X-5)=2X²-7X-15]
And since (X+1.5)(X-5)=0, there are only two answers, since one of the brackets must equal 0.
X=-1.5, X=5.
QED.
G
Kabz, is this 2nd year degree level in the US? At my English Grammar school I was doing this when I was 14. The second year of my degree was more along the lines of complex calculus in multiple variables. Now that I am glad not to have to do any more, 2nd order differential equations is about as hard as it gets in the real world.