The potential energy U(x) of a particle moving along x - axis is given by `U(x)=ax-bx^(2)`. Find the equilibrium position of particle.

Explanation

To find the equilibrium position of a particle moving along the x-axis with the given potential energy \( U(x) = ax - bx^2 \), we will follow these steps:

### Step-by-Step Solution:

1. **Understand the concept of equilibrium**:
The equilibrium position of a particle is where the net force acting on it is zero. In terms of potential energy, this condition is met when the derivative of the potential energy with respect to position is zero.

2. **Write the expression for force**:
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