Solve Deltax=a/frac{x{ab*sinbeta}}

$$\Delta x = \frac { a } { \frac { x } { a b \times \sin \beta } }$$

Solve for b (complex solution)

$$b=\frac{\Delta x^{2}}{a^{2}\sin(\beta )}$$

$$x\neq 0\text{ and }\Delta \neq 0\text{ and }a\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\beta =\pi n_{1}$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Divide a by \frac{x}{ab\sin(\beta )} by multiplying a by the reciprocal of \frac{x}{ab\sin(\beta )}.

$$\Delta x=\frac{aab\sin(\beta )}{x}$$

Multiply a and a to get a^{2}.

$$\Delta x=\frac{a^{2}b\sin(\beta )}{x}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{a^{2}b\sin(\beta )}{x}=\Delta x$$

Multiply both sides of the equation by x.

$$a^{2}b\sin(\beta )=\Delta xx$$

Multiply x and x to get x^{2}.

$$a^{2}b\sin(\beta )=\Delta x^{2}$$

The equation is in standard form.

$$a^{2}\sin(\beta )b=\Delta x^{2}$$

Divide both sides by a^{2}\sin(\beta ).

$$\frac{a^{2}\sin(\beta )b}{a^{2}\sin(\beta )}=\frac{\Delta x^{2}}{a^{2}\sin(\beta )}$$

Dividing by a^{2}\sin(\beta ) undoes the multiplication by a^{2}\sin(\beta ).

$$b=\frac{\Delta x^{2}}{a^{2}\sin(\beta )}$$

Variable b cannot be equal to 0.

$$b=\frac{\Delta x^{2}}{a^{2}\sin(\beta )}\text{, }b\neq 0$$

Solve for b

$$b=\frac{\left(\frac{x}{a}\right)^{2}\Delta }{\sin(\beta )}$$

$$x\neq 0\text{ and }a\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\beta =\pi n_{1}\text{ and }\Delta \neq 0$$

Steps for Solving Linear Equation

Variable b cannot be equal to 0 since division by zero is not defined. Divide a by \frac{x}{ab\sin(\beta )} by multiplying a by the reciprocal of \frac{x}{ab\sin(\beta )}.

$$\Delta x=\frac{aab\sin(\beta )}{x}$$

Multiply a and a to get a^{2}.

$$\Delta x=\frac{a^{2}b\sin(\beta )}{x}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{a^{2}b\sin(\beta )}{x}=\Delta x$$

Multiply both sides of the equation by x.

$$a^{2}b\sin(\beta )=\Delta xx$$

Multiply x and x to get x^{2}.

$$a^{2}b\sin(\beta )=\Delta x^{2}$$

The equation is in standard form.

$$a^{2}\sin(\beta )b=\Delta x^{2}$$

Divide both sides by a^{2}\sin(\beta ).

$$\frac{a^{2}\sin(\beta )b}{a^{2}\sin(\beta )}=\frac{\Delta x^{2}}{a^{2}\sin(\beta )}$$

Dividing by a^{2}\sin(\beta ) undoes the multiplication by a^{2}\sin(\beta ).

$$b=\frac{\Delta x^{2}}{a^{2}\sin(\beta )}$$

Variable b cannot be equal to 0.

$$b=\frac{\Delta x^{2}}{a^{2}\sin(\beta )}\text{, }b\neq 0$$

Solve for a (complex solution)

$$a=-ib^{-\frac{1}{2}}\sqrt{\Delta }x\left(-\sin(\beta )\right)^{-\frac{1}{2}}$$

$$a=ib^{-\frac{1}{2}}\sqrt{\Delta }x\left(-\sin(\beta )\right)^{-\frac{1}{2}}\text{, }x\neq 0\text{ and }b\neq 0\text{ and }\Delta \neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\beta =\pi n_{1}$$