What is the value of the descriminant of 2x2-13x-7=0? And what can you learn to know about the roots from that value?

For the equation ax²+bx+c, the discriminant is the expression b²-4ac, which amounts to

(-13)²-4*2*(-7)
=169+56
=225
=15²

The fact that the discriminant is a perfect square means that solutions are integers/rational numbers, which also means that there are two distinct real rational factors/roots.