HELP GEOMETRY

Point F lies in △ABC, such that the extension of BF intersect AC at E, the extension of CF intersect AB at D. Suppose the areas of △BDF, △CEF, quadrilateral ADFE are 2, 3, 4, respectively. The area of △BFC is $\frac{3+3\sqrt{M}}{2}$ where M is an integer. Find M.