Nothing is wrong with your reasoning, you may have erred on your use of the quadratic formula. Common errors could include forgetting that -b is positive if b is negative, that -4ac is negative if a and c are both negative, that 2a is negative if a is negative, or that b^2 is always positive. Without knowing what answers you got, it's impossible to trace further.
ETA: Unless I mistyped, you should get 410 +/- 30 sqrt 137, which are about 761 and 59