Sacred Haven of Debauchery

AntiCrab, a joke repeated twice becomes a cliché.

for what values of a, does the equation 2x²+(a³+8a-1)x+a-4=0 have roots with different signs?

I don't remember exactly how to solve this. We did a lot of such problems in class, but I've forgotten. Find the discriminant and analyze it. The discriminant must be greater than zero, and the product of the roots must be less than zero. Find the values of 'a' based on these conditions.