Arithmetic Sequences Question

The sum of the first three terms of an arithmetic sequence is 15. The sum of their squares is 147. Determine the sequence.

I know the answer by trial and error, but I need an algebraic method of solving it. Would I just make 2 equations from the information given, and solve it as a linear system? Or is there an easier way?

a = m
b = m + d
c = m + 2d

a + b + c = 15
m + m + d + m = 2d = 15
3m + 3d = 15
m + d = 5

a^2 + b^2 + c^2 = 147
m^2 + (m + d)^2 + (m + 2d)^2 = 147
m^2 + m^2 + 2md + d^2 + m^2 + 4md + 4d^2 = 147
3m^2 + 6md + 5d^2 = 147

m = 5 - d

3 * (5 - d)^2 + 6 * (5 - d) * d + 5 * d^2 = 147
3 * (25 - 10d + d^2) + (30 - 6d) * d + 5d^2 = 147
75 - 30d + 3d^2 + 30d - 6d^2 + 5d^2 = 147
2d^2 = 72
d^2 = 36
d = +/- 6

m = 5 - d
m = 5 +/- 6
m = -1 , 11

-1 , 5 , 11

There's your sequence