Find all values of j for which the quadratic equation has two real solutions

Question

2x²+7x+j = 0

Answer 1

The condition for real roots is that the quadratic formula discriminant is greater that zero.

For this equation that is the square root of 49--8j and this is greater than zero if j is less than or equal to 49/8

Any value of j greater than that will result in complex roots!