The direct-current circuit shown contains three parallel branches connected across two common conducting rails. The left branch contains an ideal battery of electromotive force \(\mathcal{E}_1 = 30\text{ V}\) and a resistor \(R_1 = 5.0\text{ }\Omega\), carrying an upward current of \(I_1 = 2.0\text{ A}\). The middle branch contains a resistor \(R_2 = 8.0\text{ }\Omega\) and an ideal battery of electromotive force \(\mathcal{E}_2 = 12\text{ V}\), carrying a downward current of \(I_2 = 1.0\text{ A}\). The right branch contains a resistor \(R_3 = 4.0\text{ }\Omega\) in series with an unknown ideal battery of electromotive force \(\mathcal{E}_x\). What is the electromotive force \(\mathcal{E}_x\) of the battery in the right branch?