Solve x^2-x/c-x-2/2=3-x/2

$$\frac { x ^ { 2 } - x } { c } - \frac { x - 2 } { 2 } = \frac { 3 - x } { 2 }$$

Solve for c

$$c=2x\left(x-1\right)$$

$$x\neq 1\text{ and }x\neq 0$$

Steps for Solving Linear Equation

Variable c cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2c, the least common multiple of c,2.

$$2\left(x^{2}-x\right)-c\left(x-2\right)=c\left(3-x\right)$$

Use the distributive property to multiply 2 by x^{2}-x.

$$2x^{2}-2x-c\left(x-2\right)=c\left(3-x\right)$$

Use the distributive property to multiply c by x-2.

$$2x^{2}-2x-\left(cx-2c\right)=c\left(3-x\right)$$

To find the opposite of cx-2c, find the opposite of each term.

$$2x^{2}-2x-cx+2c=c\left(3-x\right)$$

Use the distributive property to multiply c by 3-x.

$$2x^{2}-2x-cx+2c=3c-cx$$

Subtract 3c from both sides.

$$2x^{2}-2x-cx+2c-3c=-cx$$

Combine 2c and -3c to get -c.

$$2x^{2}-2x-cx-c=-cx$$

Add cx to both sides.

$$2x^{2}-2x-cx-c+cx=0$$

Combine -cx and cx to get 0.

$$2x^{2}-2x-c=0$$

Subtract 2x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-2x-c=-2x^{2}$$

Add 2x to both sides.

$$-c=-2x^{2}+2x$$

The equation is in standard form.

$$-c=2x-2x^{2}$$

Divide both sides by -1.

$$\frac{-c}{-1}=\frac{2x\left(1-x\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$c=\frac{2x\left(1-x\right)}{-1}$$

Divide 2x\left(1-x\right) by -1.

$$c=-2x\left(1-x\right)$$

Variable c cannot be equal to 0.

$$c=-2x\left(1-x\right)\text{, }c\neq 0$$

Solve for x (complex solution)

$$x=\frac{\sqrt{2c+1}+1}{2}$$

$$x=\frac{-\sqrt{2c+1}+1}{2}\text{, }c\neq 0$$

Solve for x

$$x=\frac{\sqrt{2c+1}+1}{2}$$

$$x=\frac{-\sqrt{2c+1}+1}{2}\text{, }c\geq -\frac{1}{2}\text{ and }c\neq 0$$