It is easy to know that BD = 14, and the direction of passing through F is the vertical line FO, passing through BD and O.

Because BF = df

So bo = do

It is easy to know that triangle DFO is similar to triangle ABD.

So DO/AD=DF/BD

That is, 7/ 10 = DF/ 14 and DF = 49/5.

Because he divided DBC equally.

So < CBE = < FBG = 1/2.

So BG split the FBD equally.

So DG/FG=BD/BF.

That is, DG/(49/5-DG) = 14/(49/5) and DG = 98/ 17.

Ask if you don't understand.