Optimizing Distance from a Cannon: Simplifying the Quadratic Formula

[kalpalned]

Homework Statement

Homework Equations

Hint given in problem statement
Quadratic formula

The Attempt at a Solution

The correct answer is theta = 70.5 degrees. I'd like to know if I'm on the right track. Do I simply solve for theta? Is there a better approach that circumvents all of this messy algebra? Much appreciated!

 

[Cutter Ketch]

Oops! All wrong. My bad. Please ignore

 

[haruspex]

Is there a better approach that circumvents all of this messy algebra?

You do not need to solve the quadratic. If r is always increasing the quadratic has no solutions. What condition on the parameters leads to that?