Finding equilibrium concentrations in solution from initial reagent concentrations and equilibrium constant We have the following reaction:
$$\ce{A + B&lt;=&gt;2C +D}$$
The initial concentration of $\ce{A}$ and $\ce{B}$ are $\pu{1M}$ each. $K_c$ is $\pu{1.0E8}$. Find the equilibrium concentration of $\ce{A}$.

This is what I have tried:
The initial concentration of A,B,C,D are 1,1,0,0 respectively
The final concentrations of A,B,C,D have to be ($1-\alpha$), ($1-\alpha$), $2\alpha$, $\alpha$ respectively. Therefore
$$K_c=\frac{[C]^c[D]^d}{[A]^a[B]^b}$$
$$10^8=\frac{(2\alpha)^2\alpha}{(1-\alpha)^2}$$
$$10^8(1-\alpha)^2=4\alpha^3$$
But even on solving this cubic equation on a calculator, the values are incorrect.
No need for the cubic equation. Just firstly assume that $\ce{A}$ and $\ce{B}$ reacted completely, then $\ce{[C]}=\pu{2M}$, $\ce{[D]}=\pu{1M}$, and from $K_c$ you can calculate $\ce{A}$ which is the same as $\ce{B}$.
That's the approximation usually used with this kind of problem.
The answer should be $\pu{2E-4M}$.