The line LH bisects segment GK, this means that it divides segment GK exactly trough its midpoint.
Segments GL is equal to segment LK and both add up to GK:
GK= GL + LK
GL=LK= 5x-5
Using this equality you have to replace the segments names by the given expressions and clear the value of x.
[tex]\begin{gathered} GK=GL+LK \\ 8x+6=(5x-5)+(5x-5) \\ 8x+6=5x-5+5x-5 \\ 8x+6=10x-10 \\ 8x-10x=-10-6 \\ -2x=-16 \\ x=8 \end{gathered}[/tex]Now you can use the value of x to calculate the length of GK
GK=8x+6=8*8+6=70
