Finally, I was able to solve the problem by using fsolve command.

Thank you very much for your help!

@Carl Love 

Thanks a lot for your information :)

I'll try the fsolve and DirectSearch functions once. Nevertheless the problem remains, please let me upload the whole program code. Thank you

@Mac Dude

Thank you so much for your advice :)

Of course, I should try to find out what the underlying problem is, and divide the problem into some parts and solve the problem step by step...however, still I don't know what I should do for this problem.

Please let me explain more detail about the problem.

In the case I posted, the degree of the equations is 7. To simplify, the degree is 3 here.

Here is a standard cubic equation:
x^3 + A*x^2 + B*x + C = 0
Let the solutions of above the equation be p1,p2 and p3, we obtain

A = -(p1+p2+p3)
B = p1*p2+p2*p3+p3*p1
C = -p1*p2*p3

If p1,p2 and p3 can be set constant values arbitrarily, and A,B and C are functions of a,b and c, we can determine the values of a,b and c by solving simultaneous equation, that is, a,b and c are variables.

For example:
When the A,B,C,p1,p2 and p3 are defined as follows,

A = 2a + b + 3c
B = ab + 2bc
C = abc
p1 = 0.1 + 0.5*i (i means an imaginary unit)
p2 = 0.1 - 0.5*i
p3 = 0.3

following formulas are established:

2a + b + 3c = -0.5
ab + 2bc = 0.32
abc = -0.078

Above the simultaneous equation gives us the values of a,b and c.

Exactly what I want to solve is 7th order equation like the same method as mentioned above.

So the problem is complex due to high degree and it is quite difficult to simplify in my view, however there might be a good way. I totally don't know because I have poor knowledge about mathematics...I'm sorry.

Could you tell me if you have any good idea?

Thank you in advance.