$$ 2\cdot \left(a-1\right)^2 - \left(a+1\right)^2 = \left(a-7\right)^2 \\ \left(a-1\right)^2 - \left(a+1\right)^2 = \left(a-7\right)^2 - \left(a-1\right)^2 \\ \left(\left(a-1\right) - \left(a+1\right)\right) \cdot \left(\left(a-1\right) + \left(a+1\right)\right)\\\quad = \left(\left(a-7\right) - \left(a-1\right)\right) \cdot \left(\left(a-7\right) + \left(a-1\right)\right) \\ -2 \cdot 2a = -6 \cdot \left(2a-8 \right) \\ -4a = -12a+48 \\ 8a = 48 \\ a = 6. $$