Solve Bx^2-(B-2)x+2=0

$$B x ^ { 2 } - ( B - 2 ) x + 2 = 0$$

Solve for B

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

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

Steps for Solving Linear Equation

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

$$Bx^{2}-\left(Bx-2x\right)+2=0$$

To find the opposite of Bx-2x, find the opposite of each term.

$$Bx^{2}-Bx+2x+2=0$$

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

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

Subtract 2 from both sides.

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

Combine all terms containing B.

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

Divide both sides by x^{2}-x.

$$\frac{\left(x^{2}-x\right)B}{x^{2}-x}=\frac{-2x-2}{x^{2}-x}$$

Dividing by x^{2}-x undoes the multiplication by x^{2}-x.

$$B=\frac{-2x-2}{x^{2}-x}$$

Divide -2x-2 by x^{2}-x.

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{B^{2}-12B+4}+B-2}{2B}\text{; }x=\frac{-\sqrt{B^{2}-12B+4}+B-2}{2B}\text{, }&B\neq 0\\x=-1\text{, }&B=0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{B^{2}-12B+4}+B-2}{2B}\text{; }x=\frac{-\sqrt{B^{2}-12B+4}+B-2}{2B}\text{, }&\left(B\neq 0\text{ and }B\leq 6-4\sqrt{2}\right)\text{ or }B\geq 4\sqrt{2}+6\\x=-1\text{, }&B=0\end{matrix}\right.$$