that said if you really insist on solving it with something directly related to X+Y=B, XY=AC you can do this
X = U+V
Y = U-V
X+Y = (U+V)+(U-V) = 2U = B
U = B/2
XY = (U+V)(U-V) = U^2 - V^2 = AC
(B/2)^2 - V^2 = AC
(B/2)^2 = AC + V^2
(B/2)^2 - AC = V^2
V =
sign makes no difference so take +
X =
Y =
