IC Timer 555 Astable Multivibrator 50% Duty cycle
Calculate the Thévenin equivalent voltage. The equivalent resistance is R1||R2 when /DISCHARGE is low. 

The duty cycle will only be 50% for a certain ratio of R1/R2. 

You will then know the starting voltage, and the end voltage (2/3 and 1/3 Vcc respectively) and you will know the Thévenin equivalent voltage and resistance and you can calculate what ratio is required to get a 50% duty cycle. 



Okay, so the capacitor charges from \$V_I\$ to \$V_F\$ with time constant \$\tau = C2 \cdot R1||R2\$ 

If we have the /DISCHARGE pin go low at t = 0 we have: 

\$v(t) = V_I + (V_F-V_I)\cdot (1-e^{t/\tau})\$ 

Substituting you get 

\$t_D = \tau\ln(\frac{R1-2R2}{2R1-R2})\$

Which results in a nonlinear equation such that R1/R2 ~= 0.423 for 50% duty cycle.