Thank You Sir

Hi Dia,

I suggest to use for your notations lowercase letters. It is a convention in Wolfram Language for users to use names which begin with lowercase letters.

So, we define the function $f[a]$, define user's parameters and plot the function:

f[a_] := \[Epsilon] (9/16 g \[Gamma] a^3 - g \[Alpha] - 1)
\[Alpha] = 1; \[Epsilon] = 0.014; \[Gamma] = 0.07; g = 2.5;
Plot[f[a], {a, -5, 5}]

We can use the function $Solve[ ]$ to obtain the roots of the equation $f[a]=0$

In[30]:= Solve[f[a] == 0, a]
Out[30]= {{a -> -1.64414 - 2.84774 I}, {a -> -1.64414 +  2.84774 I}, {a -> 3.28828}}

There are two complex roots and one real.

Thank you for responding, actually I want to plot f(A^2) with respect to A^2.

Hi Dia, Your problem is somewhat unclear. Nevertheless, I hope to understand your requests as close as possible. Firstly, we need to define the function $f[a]$ as:

f[a_] := G (1 - a/4 + \[Alpha] a^2/8 - 5 \[Gamma] a^3/64) - d

Your $F[A^2]$ is obtained as

In[2]:= f[A^2]
Out[2]= -0.2 + 0.1 (1 - A^2/4 + 0.01425 A^4 - 0.000234375 A^6)

Let us define the parameters:

\[Alpha] = 0.114;
\[Gamma] = 0.003; G = 0.1; d = 0.2;

Now, the graphs may be plot:

Plot[{f[A^2], Sqrt[A], -Sqrt[A]}, {A, 0, 9}, PlotStyle -> {Red, Blue, Blue}]