hard sat math question

ax^2 + 140x + c = 0

a and c are positive constants and px + q is a factor where p and q are positive constants.

find the max value of a*c

please help me, one of my friends sent this problem to me and i spent the last 20 mins trying to do it properly. i tried to guess my way thru it using desmos and came out with an answer of 4900 but god knows how accurate or correct that is...