X horsepower is equal an 20lb. Object traveling at 90mph. Is it possible to solve for X? and if so, what does X equal?

If that 20 pounds is the constant force on the object, for example it is moving down under gravity, then yes force*speed in the direction of force = power.

However if the 20 pounds is just a way to say what the mass of the object is on earth and it is not moving straight down at constant speed, then no. In that case we can compute kinetic energy (1/2)mv^2 but not power.