The number of solutions of a quadratic equation
[tex]ax^2+bx+c=0[/tex]
Depends on its discriminant
[tex]\Delta = b^2-4ac[/tex]
- If [tex]\Delta>0[/tex] there are two distinct solutions
- If [tex]\Delta=0[/tex] there are two coincident solutions
- If [tex]\Delta<0[/tex] there are no solutions.
We know that there are two real solutions (I assume you mean distinct solutions), so we know that the discriminant is positive:
[tex]b^2-4ac = 9+28t > 0 \iff t>-\dfrac{9}{28}[/tex]
