Solve C(x)/x=-x^2+7x-10

$$\frac { C ( x ) } { x } = - x ^ { 2 } + 7 x - 10$$

Solve for C

$$C=-\left(x-5\right)\left(x-2\right)$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$Cx=-xx^{2}+7xx+x\left(-10\right)$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$Cx=-x^{3}+7xx+x\left(-10\right)$$

Multiply x and x to get x^{2}.

$$Cx=-x^{3}+7x^{2}+x\left(-10\right)$$

The equation is in standard form.

$$xC=-x^{3}+7x^{2}-10x$$

Divide both sides by x.

$$\frac{xC}{x}=\frac{x\left(2-x\right)\left(x-5\right)}{x}$$

Dividing by x undoes the multiplication by x.

$$C=\frac{x\left(2-x\right)\left(x-5\right)}{x}$$

Divide x\left(-5+x\right)\left(2-x\right) by x.

$$C=\left(2-x\right)\left(x-5\right)$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=\frac{\sqrt{9-4C}+7}{2}\text{, }&\text{unconditionally}\\x=\frac{-\sqrt{9-4C}+7}{2}\text{, }&C\neq -10\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{-\sqrt{9-4C}+7}{2}\text{, }&C\neq -10\text{ and }C\leq \frac{9}{4}\\x=\frac{\sqrt{9-4C}+7}{2}\text{, }&C\leq \frac{9}{4}\end{matrix}\right.$$