The revenue made from selling $x$ units of a coffee maker is given by $R=-0.37 x^{2}+61 x$. It costs the manufacturer $C=-0.17 x^{2}+17 x+620$ dollars to make $x$ units of this particular coffee maker. Write an equation describing the profit $(P)$ made from selling $x$ units of the coffee maker in this market. Enter your answer in simplified form. The simplified equation for the profit $(P)$ from selling $x$ units is given by: \[ P= \]

Step 1 ：The revenue made from selling \(x\) units of a coffee maker is given by \(R=-0.37 x^{2}+61 x\). It costs the manufacturer \(C=-0.17 x^{2}+17 x+620\) dollars to make \(x\) units of this particular coffee maker. We are asked to write an equation describing the profit \((P)\) made from selling \(x\) units of the coffee maker in this market.

Step 2 ：The profit made from selling a certain number of units is given by the revenue from selling those units minus the cost of producing those units. Therefore, we can find the equation for the profit by subtracting the cost equation from the revenue equation.

Step 3 ：Subtracting the cost equation from the revenue equation, we get \(P = R - C = (-0.37x^{2} + 61x) - (-0.17x^{2} + 17x + 620) = -0.2x^{2} + 44x - 620\).

Step 4 ：\(\boxed{P=-0.2 x^{2}+44 x-620}\) is the simplified equation for the profit \((P)\) from selling \(x\) units of the coffee maker in this market.