Verified answer

n^2 + (n+2)^2 + (n+4)^2 = 776

n^2 + n^2 + 4n + 4 + n^2 + 8n + 16 = 776

3n^2 +12n + 20 = 776

3n^2 +12n - 756 = 0

n^2 + 4n - 252 = 0

(x + 18)(x - 14) = 0

La solución positiva es x = 14

Comprobar:

14^2 + 16^2 + 18^2 = 776

196 + 256 + 324 = 776

776 = 776

Verdad!

La solución negativa funciona también

(-18)^2 + (-16)^ + (-14)^2 = 776

324 + 256 + 192 = 776

776 = 776

(2x)^2 + (2x + 2)^2 + (2x + 4)^2 = 776

4x^2 + 4x^2 + 8x + 4 + 4x^2 + 16x + 16 = 776

12x^2 + 24x - 756 = 0

x = 7 or -9

The sets of three would be 14, 16, 18 or -18, -16, -14

Edit: Sorry, missed the sum of "squares" part