Solve x/40-beta/x=92^circ-x

$$\frac { x } { 40 } - \frac { \beta } { x } = 92 ^ { \circ } - x$$

Solve for β

$$\beta =\frac{x\left(41x-3680\right)}{40}$$

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 40x, the least common multiple of 40,x.

$$xx-40\beta =40x\times 92-x\times 40x$$

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

$$x^{2}-40\beta =40x\times 92-x\times 40x$$

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

$$x^{2}-40\beta =40x\times 92-x^{2}\times 40$$

Multiply 40 and 92 to get 3680.

$$x^{2}-40\beta =3680x-x^{2}\times 40$$

Multiply -1 and 40 to get -40.

$$x^{2}-40\beta =3680x-40x^{2}$$

Subtract x^{2} from both sides.

$$-40\beta =3680x-40x^{2}-x^{2}$$

Combine -40x^{2} and -x^{2} to get -41x^{2}.

$$-40\beta =3680x-41x^{2}$$

Divide both sides by -40.

$$\frac{-40\beta }{-40}=\frac{x\left(3680-41x\right)}{-40}$$

Dividing by -40 undoes the multiplication by -40.

$$\beta =\frac{x\left(3680-41x\right)}{-40}$$

Divide x\left(3680-41x\right) by -40.

$$\beta =\frac{41x^{2}}{40}-92x$$

Solve for x

$$\left\{\begin{matrix}x=\frac{-2\sqrt{410\beta +846400}+1840}{41}\text{, }&\beta \neq 0\text{ and }\beta \geq -\frac{84640}{41}\\x=\frac{2\sqrt{410\beta +846400}+1840}{41}\text{, }&\beta \geq -\frac{84640}{41}\end{matrix}\right.$$