History of Hindu Mathematics: A Source Book v2.c17.s8.7

v2.c17.s8.7

If *x* be the number of days after which the first overtakes the second, then we shall have $S(t + x) = x s + ( (x - 1)/2 ) b ,$ or $bx² - 2(S - s) + bx = 2tS.$ Therefore $x = (√(2(S - s) + b² + 8btS) + 2(S - s) + b)/2b,$ which agrees exactly with the solution as stated in the Bakhshâlî treatise.