You have to solve for x first before you can find the length of BD.
BE = DE
Plug in
10x - 3 = 8x -1
+3 +3
------------------------
10x = 8x + 2
-8x -8x
------------------------
2x = 2
2x ÷ 2 = 2 ÷ 2
-------------------------
x = 1
Then you Plug in again
BE + DE = BD
10x - 3 + 8x - 1 = BD
10(1) - 3 + 8(1) - 1= BD
10 - 3 + 8 - 1= BD
7 + 7 = BD
14 = BD
BD = 14