v+2/v+4/(3v)=11, multiply through by 3v:
3v2+6+4=33v,
3v2-33v=-10,
v2-11v=-10/3,
v2-11v+121/4=121/4-10/3,
(v-11/2)2=(363-40)/12=323/12,
v-11/2=±√(323/12), v=11/2±5.1881 approx.
v=10.6881 or 0.3119.
Another interpretation: v+2/v+(4/3)v=11, multiply through by v:
v2+2+(4/3)v2=11v,
(7/3)v2-11v+2=0,
7v2-33v+6=0,
v=(33±√(1089-168))/14=4.5249 or 0.1894 approx.