the discriminant tells or discriminates how many roots there will be and what kind they are
that is the bit under the square root sign with is b^2-4ac
when you have
ax^2+bx+c=0
we have
2x^2+1x-3=0
a=2
b=1
c=-3
sub
b^2-4ac
1^2-4*2*-3
1+24
25
the discriminant is 25 C