Breaking a proof between frames [closed]

Question

I have the same question in here

Proofs in Beamer

In the answer, the author used beamertemplate to examine breaking the frames. But how can i change it to my paragraph?

For example, i need to insert the following problem and its solution

Problem : Solve x^{3} - x -3=2\sqrt[3]{6x-3x^{2}}

Proof : Put a:=\sqrt[3]{6x-3x^2} to obtain a system

\begin{eqnarray}x^3-x-3 &=& 2a\\6x-3x^2 &=& a^3\end{eqnarray}

Add the equations up to get

x^3-3x^2+5x-3=a^3+2a

(x-1)^3+2(x-1)=a^3+2a

Put y:=x-1 to get

y^3+2y=a^3+2a

(y-a)(y^2+ay+a^2+2)=0

The second factor is obviously always positive, hence y=a\iff a=x-1

Now (1) yields x^3-x-3=2x-2\iff x^3-3x=1

Put x:=2t to get

8t^3-6t=1\iff 4t^3-3t={1\over 2}

By addition formulas, there must exist \phi such that t=\cos\phi, yielding

\cos 3\phi={1\over 2}\iff 3\phi=\pm{\pi\over 3}+2k\pi\iff \phi=\pm{\pi\over 9}+{2k\pi\over 3},k\in\mathbb{Z}

Now x=2\cos\phi=2\cos\left(\pm{\pi\over 9}+{2k\pi\over 3}\right), i.e.

x\in\left\{2\cos{\pi\over 9},2\cos{5\pi\over 9},2\cos{7\pi\over 9}\right\}

It may take more than one frame and i think the command allowbreakframes is useful. But i don't know how to exchange beamertemplate to my above paragraph. I also want to put the problem and the solution in blocks. Thanks for your listening my question!