Find the product of all positive integer values of $c$ such that the quadratic equation $3x^2+7x+c=15x-10$ has two real roots.
Rearrange as
3x^2 -8x + c + 10
This will have two real roots when the discriminant > 0
So
(-8)^2 - 4 (3) (c + 10) > 0
64 -120 > 12c
-56 > 12c
c < -56 / 12
c < -14/3
There are no positive integer values for c that give two real roots !!!
+1348 
