Formula Derivation:
$ I_i = \frac{0 - v_i}{R_i} $
$ I_f = \frac{v_i - v_o}{R_f} $
since, there is no current flow between positive and negative pins,
$ I_i = I_f $
Now,
\begin{align}
\frac{0 - v_i}{R_i} & = \frac{v_i - v_o}{R_f} \\
\frac{- v_i}{R_i} & = \frac{v_i - v_o}{R_f} \\
- v_i & = \frac{R_i}{R_f}(v_i - v_o) \\
\frac{R_f}{R_i} & = \frac{(v_i - v_o)}{- v_i} \\
\frac{R_f}{R_i} & = - 1 + \frac{v_o}{v_i} \\
\frac{v_o}{v_i} & = \frac{R_f}{R_i} + 1 \\
v_o & = v_i ( 1 + \frac{R_f}{R_i} )
\end{align}
The output voltage formula,
$ v_o = v_i ( 1 + \frac{R_f}{R_i} ) $
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