Solve s(2x-s)/3=x-1/2

$$\frac { s ( 2 x - s ) } { 3 } = \frac { x - 1 } { 2 }$$

Solve for x

$$x=-\frac{3-2s^{2}}{4s-3}$$

$$s\neq \frac{3}{4}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2s\left(2x-s\right)=3\left(x-1\right)$$

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

$$4xs-2s^{2}=3\left(x-1\right)$$

Use the distributive property to multiply 3 by x-1.

$$4xs-2s^{2}=3x-3$$

Subtract 3x from both sides.

$$4xs-2s^{2}-3x=-3$$

Add 2s^{2} to both sides.

$$4xs-3x=-3+2s^{2}$$

Combine all terms containing x.

$$\left(4s-3\right)x=-3+2s^{2}$$

The equation is in standard form.

$$\left(4s-3\right)x=2s^{2}-3$$

Divide both sides by 4s-3.

$$\frac{\left(4s-3\right)x}{4s-3}=\frac{2s^{2}-3}{4s-3}$$

Dividing by 4s-3 undoes the multiplication by 4s-3.

$$x=\frac{2s^{2}-3}{4s-3}$$

Solve for s

$$s=-\frac{\sqrt{4x^{2}-6x+6}}{2}+x$$

$$s=\frac{\sqrt{4x^{2}-6x+6}}{2}+x$$