I am having a hard time figuring out how to solve for the vo

I am having a hard time figuring out how to solve for the voltage across the capacitor C1 and C2. I know the lab that the voltage for C1 and C2 is 4.5 volts but i am unsure of how to get there with the math.

Question

V₀ = 9 Volts, C₁ = 0.1 F, C₂ = 0.1 F, C₃ = 0.05 F.

Sharing the charge stored on C₁ with capacitor C₂ (initially discharged) ? keep switch W₃ still open; open switch W₁ and close switch W₂. Measure voltage V₂ across capacitors C₁ and C₂ and calculate the amount of charges stored on each of them, Q₁₂ = C₁V₂ and Q₂ = C₂V₂ . Knowing the values of capacitance C₁ and C₂ and the initial charge Q₁ stored on C₁, calculate the theoretically expected voltage V_2Theory after capacitor C₂ got connected in parallel with C₁.

Solution

common voltage =[ C1xV1+ C2 x 0]/(C1+C2)= V1/2=9/2=4.5 V