To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints using mathematical notation.

Let's denote:
- $x_1$ as the milligrams of vitamin K,
- $x_2$ as the milligrams of vitamin B3.

The objective function to minimize is given by:
\[3.72x_1^2 + 4.42x_1x_2 + 7.14x_2^2 + 5.68x_1 + 3.49x_2\]

The constraints are as follows:
1. The energy stability index for vitamin K is 8, and for vitamin B3 is also 8. However, these values seem to be part of a larger constraint involving the total combined energy stability index.
2. The total combined energy stability index from milligrams of vitamin K squared plus milligrams of vitamin B3 squared must be at least 51: \[x_1^2 + x_2^2 \geq 51\]
3. The total combined energy stability index from milligrams of vitamin K and milligrams of vitamin B3 should be no less than 51. This seems to imply a linear combination, but given the context, it might mean: \[8x_1 + 8x_2 \geq 51\]
4. Minus two times the number of milligrams of vitamin K plus five times the number of milligrams of vitamin B3 has to be at least zero: \[-2x_1 + 5x_2 \geq 0\]
5. The total combined energy stability index from milligrams of vitamin K and milligrams of vitamin B3 must be at most 67: \[8x_1 + 8x_2 \leq 67\]
6. $x_1$ is an integer (milligrams of vitamin K).
7. $x_2$ can be any real number (milligrams of vitamin B3).

Thus, the symbolic representation of the problem in JSON format is:
```json
{
  'sym_variables': [('x1', 'milligrams of vitamin K'), ('x2', 'milligrams of vitamin B3')],
  'objective_function': '3.72*x1**2 + 4.42*x1*x2 + 7.14*x2**2 + 5.68*x1 + 3.49*x2',
  'constraints': [
    'x1**2 + x2**2 >= 51',
    '8*x1 + 8*x2 >= 51',
    '-2*x1 + 5*x2 >= 0',
    '8*x1 + 8*x2 <= 67'
  ]
}
```

Now, to solve this problem using Gurobi, we can write the following Python code:
```python
from gurobipy import *

# Create a new model
m = Model("Vitamin_Optimization")

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="milligrams_of_vitamin_K")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_B3")

# Set the objective function
m.setObjective(3.72*x1**2 + 4.42*x1*x2 + 7.14*x2**2 + 5.68*x1 + 3.49*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(x1**2 + x2**2 >= 51, "total_energy_stability_index_squared")
m.addConstr(8*x1 + 8*x2 >= 51, "total_energy_stability_index")
m.addConstr(-2*x1 + 5*x2 >= 0, "vitamin_balance")
m.addConstr(8*x1 + 8*x2 <= 67, "max_total_energy_stability_index")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Milligrams of Vitamin K: {x1.x}")
    print(f"Milligrams of Vitamin B3: {x2.x}")
    print(f"Objective Function Value: {m.objVal}")
else:
    print("No optimal solution found")
```