Solve 1-2v^2/8x=3*1/2

$$1 - 2 v ^ { 2 } / 8 x = 3 \times \frac { 1 } { 2 }$$

Solve for x

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

$$v\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8, the least common multiple of 8,2.

$$8-2v^{2}x=24\times \frac{1}{2}$$

Multiply 24 and \frac{1}{2} to get 12.

$$8-2v^{2}x=12$$

Subtract 8 from both sides.

$$-2v^{2}x=12-8$$

Subtract 8 from 12 to get 4.

$$-2v^{2}x=4$$

The equation is in standard form.

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

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

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

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

$$x=\frac{4}{-2v^{2}}$$

Divide 4 by -2v^{2}.

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

Solve for v (complex solution)

$$v=-\sqrt{2}ix^{-\frac{1}{2}}$$

$$v=\sqrt{2}ix^{-\frac{1}{2}}\text{, }x\neq 0$$

Solve for v

$$v=\sqrt{-\frac{2}{x}}$$

$$v=-\sqrt{-\frac{2}{x}}\text{, }x<0$$