# Finding solutions to 3 \tan^2 \theta−\tan \theta-14=0 within 0 \leq

Finding solutions to $3{\mathrm{tan}}^{2}\theta -\mathrm{tan}\theta -14=0$ within $0\le \theta \le {360}^{\circ }$
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Jason Duke

For $0\le \theta \le {360}^{\circ }$, there are only 2 solutions for $\mathrm{tan}\theta =a$ that a is a real number, except a=0, it has 3 solutions $\theta ={0}^{\circ },{180}^{\circ },{360}^{\circ }$. Therefore, you have found that $\mathrm{tan}\theta =\frac{7}{3}$ or −2, so there are 4 solutions. Then, you can find the solutions as Harshit Gupta