314₁₀ - 256₇ = 340_x,
Convert 256₇ and 340_x to base 10, such that:
314 - 139 = 3x² + 4x
=> 3x² + 4x - 175 = 0 (quadratic)
Factorising, (x - 7) (3x + 25) = 0,
either x = 7 or x = -25/3 ( but x cannot be negative)

Therefore, x = 7.