Solve (b-x)(3-2x)*1/2=9/2

$$( b - x ) ( 3 - 2 x ) \times \frac { 1 } { 2 } = \frac { 9 } { 2 }$$

Solve for b

$$b=-\frac{\left(x-3\right)\left(2x+3\right)}{3-2x}$$

$$x\neq \frac{3}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply b-x by 3-2x.

$$\left(3b-2bx-3x+2x^{2}\right)\times \frac{1}{2}=\frac{9}{2}$$

Use the distributive property to multiply 3b-2bx-3x+2x^{2} by \frac{1}{2}.

$$\frac{3}{2}b-bx-\frac{3}{2}x+x^{2}=\frac{9}{2}$$

Add \frac{3}{2}x to both sides.

$$\frac{3}{2}b-bx+x^{2}=\frac{9}{2}+\frac{3}{2}x$$

Subtract x^{2} from both sides.

$$\frac{3}{2}b-bx=\frac{9}{2}+\frac{3}{2}x-x^{2}$$

Combine all terms containing b.

$$\left(\frac{3}{2}-x\right)b=\frac{9}{2}+\frac{3}{2}x-x^{2}$$

The equation is in standard form.

$$\left(\frac{3}{2}-x\right)b=-x^{2}+\frac{3x}{2}+\frac{9}{2}$$

Divide both sides by \frac{3}{2}-x.

$$\frac{\left(\frac{3}{2}-x\right)b}{\frac{3}{2}-x}=\frac{-x^{2}+\frac{3x}{2}+\frac{9}{2}}{\frac{3}{2}-x}$$

Dividing by \frac{3}{2}-x undoes the multiplication by \frac{3}{2}-x.

$$b=\frac{-x^{2}+\frac{3x}{2}+\frac{9}{2}}{\frac{3}{2}-x}$$

Divide \frac{9}{2}+\frac{3x}{2}-x^{2} by \frac{3}{2}-x.

$$b=\frac{\left(3-x\right)\left(2x+3\right)}{3-2x}$$

Solve for x

$$x=\frac{\sqrt{4b^{2}-12b+81}}{4}+\frac{b}{2}+\frac{3}{4}$$

$$x=-\frac{\sqrt{4b^{2}-12b+81}}{4}+\frac{b}{2}+\frac{3}{4}$$