Solve the given equations and answer the following question.

I. z = (x + b) + (- (a)/2)

II.x3 + 514 = 8[a2 + (b + 1)2] + 290

III.6y2 + 57y − 192 = 5y2 + 3(13y − 51)

Where, 'a' and 'b' are the smaller and greater root of equation III respectively.

Find the value of R = (z/3)% of 200 + (x + 2)2 + b2)