How can you solve and equation with inverse functions?

Question

$$\arctan(x) - \arctan(2/x) = \arctan(7/9)$$ where $x$ is positive .

The answer should be 3. Thanks

Answer 1

Using $$\tan(A-B)=\frac{\tan A-\tan B}{1+\tan A\tan B}$$ we get the equation $$\frac{x-2/x}{1+2}=\frac79$$ which looks like a nice quadratic equation.

Answer 2

Using Inverse trigonometric function identity doubt: $\tan^{-1}x+\tan^{-1}y =-\pi+\tan^{-1}\left(\frac{x+y}{1-xy}\right)$, when $x<0$, $y<0$, and $xy>1$,

$$\arctan\dfrac2x+\arctan\dfrac79=\arctan\dfrac{18+7x}{9x-14}$$ for $\dfrac{2\cdot7}{x\cdot9}<1$ which happens if $x<0$ or if $x>\dfrac{14}9$

What if $\dfrac{14}{9x}\ge1?$