if Voltage source is 12, resistance is 6800 and voltage 1 is 8 what is R2

if Voltage source is 12, resistance is 6800 and voltage 1 is 8 what is R2

$$\small{\text{series circuit }}$\\$ \small{\text{$ R=6800\ \Omega \quad U = 12\ V\quad U_1 = 8\ V\quad R_2=\ ? \ \Omega $ }}$\\$ \small{\text{ I. $ \quad I=\frac{R_1}{U_1}=\frac{R_2}{U_2} \quad \Rightarrow \quad \boxed{R_2=\frac{U_2}{U_1}*R_1} $ }}$\\\\$ \small{\text{ II. $ \quad R=R_1+R_2 \quad \Rightarrow \quad \boxed{R_1=R-R_2} $ }}$\\\\$ \small{\text{ III. $ \quad U=U_1+U_2 \quad \Rightarrow \quad \boxed{U_2=U-U_1} $ }}$\\\\$ \small{\text{ we substitute $U_2=U-U_1 $ and $R_1=R-R_2$ }}$\\\\$ \small{\text{ $ R_2=\left(\frac{U-U_1}{U_1}\right) *(R-R_2)\quad \Rightarrow \quad \boxed{\textcolor[rgb]{1,0,0}{ R_2 = \left( 1-\frac{U_1}{U} \right) *R } } $ }} $\\\\$ \small{\text{ $ R_2 = \left( 1-\frac{8\ V}{12\ V} \right) * 6800 \ \Omega = \left( 1-\frac{2}{3} \right) * 6800 \ \Omega =\frac{1}{3}* 6800 \ \Omega =2266.\overline{6} \ \Omega $ }} $\\\\$ \small{\text{ $ \textcolor[rgb]{1,0,0}{R_2 = 2266.\overline{6} \ \Omega } $ }}$$

Thank you Heureka  

I am going to reference this from the LaTex page too.  Thanks again :)