Circuit analysis of series diode clipper circuit
An explicit model to be used for the diode is missing in the original question, however the diode parameters provided (\$V_d\$ and \$R_d\$) point towards using a piece-wise linear model for the diode. Therefore, your circuit should be redrawn as follows.



simulate this circuit &ndash; Schematic created using CircuitLab
Assuming \$V_{out} &gt; V_d\$, the ideal diode has a forward bias and acts as a short-circuit. Voltage equations:
$$
\frac{V_{out}-V_i}{R_1}+\frac{V_{out}-V_d}{R_d}=0
$$
With the additional constraint \$V_{out} = 0.5V_i\$:
$$
\frac{-0.5V_i}{R_1}+\frac{0.5V_i-V_d}{R_d}=0
$$
$$
0.5\left(\frac{1}{R_d}-\frac{1}{R_1}\right)V_i=\frac{V_d}{R_d}
$$
$$
V_i=2\frac{V_d}{R_d\left(\frac{1}{R_d}-\frac{1}{R_1}\right)}
$$
Checking numerically if the forward bias assumption holds true:
$$
V_i=\frac{1.4}{5(0.2-0.1)}=\frac{1.4}{0.5}=2.8
$$
$$
V_{out}=0.5V_i=1.4 &gt; V_d
$$