differential output amplifier formula derivation
Apply nodal at the non inverting and inverting termial of upper Op amp

at non inveting terminal

\$\frac{V_x-v_{in}}{Rg}+\frac{V_x-V_{out2}}{R_f}=0----------------(1)\$

at inverting terminal

\$\frac{V_x-v_{out2}}{R_4}+\frac{V_x-V_{out1}}{R_1}=0---- -----------(2)\$

Also nodal at the lower op amp inverting terminal

\$\frac{0-v_{out2}}{R_2}+\frac{0-V_{out1}}{R_3}=0---------------(3)\$

As given \$R_1=R_2=R_3=R_4=R\$

So from equation \$(3)\$

\$V_{out2}=-V_{out1}\$

and from equation \$(2)\$,\$V_x=\frac{V_{out1}+V_{out2}}{2}\$
from this \$V_x=0\$

Now from equation \$(1)\$

\$V_{out2}=-\frac{V_{in}R_f}{R_g}\$
also \$V_{out1}=\frac{V_{in}R_f}{R_g}\$

Now the desired output \$G=\frac{V_{out1}-V_{out1}}{Vin}=2\frac{R_f}{R_g}\$