Step 1 :Given the revenue equation \(R=-0.31x^{2}+55x\) and the cost equation \(C=-0.14x^{2}+14x+860\).
Step 2 :The profit equation is calculated by subtracting the cost from the revenue.
Step 3 :So, \(P=R-C\).
Step 4 :Substituting the given equations into the profit equation, we get \(P=(-0.31x^{2}+55x)-(-0.14x^{2}+14x+860)\).
Step 5 :Simplifying the equation, we get \(P=-0.17x^{2}+41x-860\).
Step 6 :So, the simplified equation for the profit \(P\) from selling \(x\) units is given by \(\boxed{P=-0.17x^{2}+41x-860}\).