R^2 + R^2 + 16R + 64 = 144

solve for R.

Gee, I didn't learn any algebra until the ninth grade. What you have can be reduced to something called the quadratic equation.

2R^2 + 16R -80 = 0
R^2 +8R -40 = 0
R = (1/2)[-8 +/-sqrt224]
= 3.4833 or -11.4833
There are no integer solutions.

Are you sure you didn't mean to write

R^2 + 16R + 64 = 144 ?
That has a simpler solution that you can get by taking the square root of each side.
(R + 8)^2 = 12^2
R = -8 +or- 12 = -20 or +4