Solve x*90/a-x=390

$$x \times 90 / a - x = 390$$

Solve for a

$$a=\frac{90x}{x+390}$$

$$x\neq 0\text{ and }x\neq -390$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$x\times 90-xa=390a$$

Subtract 390a from both sides.

$$x\times 90-xa-390a=0$$

Subtract x\times 90 from both sides. Anything subtracted from zero gives its negation.

$$-xa-390a=-x\times 90$$

Multiply -1 and 90 to get -90.

$$-xa-390a=-90x$$

Combine all terms containing a.

$$\left(-x-390\right)a=-90x$$

Divide both sides by -x-390.

$$\frac{\left(-x-390\right)a}{-x-390}=-\frac{90x}{-x-390}$$

Dividing by -x-390 undoes the multiplication by -x-390.

$$a=-\frac{90x}{-x-390}$$

Divide -90x by -x-390.

$$a=\frac{90x}{x+390}$$

Variable a cannot be equal to 0.

$$a=\frac{90x}{x+390}\text{, }a\neq 0$$

Solve for x

$$x=\frac{390a}{90-a}$$

$$a\neq 90\text{ and }a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by a.

$$x\times 90-xa=390a$$

Combine all terms containing x.

$$\left(90-a\right)x=390a$$

Divide both sides by 90-a.

$$\frac{\left(90-a\right)x}{90-a}=\frac{390a}{90-a}$$

Dividing by 90-a undoes the multiplication by 90-a.

$$x=\frac{390a}{90-a}$$