This can be written:
14x2-60x+26=0,
7x2-30x+13=0, which has no rational factors.
7x2-30x=-13,
7(x2-30x/7)=-13,
7(x2-30x/7+(15/7)2-(15/7)2)=-13,
7(x-15/7)2-225/7=-13,
7(x-15/7)2=225/7-13=(225-91)/7=134/7,
(x-15/7)2=134/49,
x-15/7=√134/7 or -√134/7,
x=(15±√134)/7=3.7965 or 0.4892 approx.
Doesn't seem to be associated with the triangle angle bisector theorem.