(I'm Overwhelmed) Algebra Progress Quiz #4 (Version 2) Q8

GRE Quant Problem Solving
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Can this problem be solved using the discriminant method?

greg did it by finding out multiples of 10 and they don’t add up to 8.

I did it the following way -
b^2-4ac = 8^2-4(1)(10) = 64-40 = 24 and since 24>0 I though this had 2 solutions.

Please advice and let me know if you need more explanation on my process.

2

Discriminant > 0 says that there are going to be 2 distinct real roots. Your question imposes another restriction (roots have to be integers), and the discriminant doesn’t account for it.