# Solve the equation: \tan^2x-3\tan x-4=0

Solve the equation:
${\mathrm{tan}}^{2}x-3\mathrm{tan}x-4=0$
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Aubree Mcintyre
Solve ${\mathrm{tan}}^{2}x-3\mathrm{tan}x-4=0$
by using inverse trigonometry
${\mathrm{tan}}^{2}x-3\mathrm{tan}x-4=0$
$\left(\mathrm{tan}x-4\right)\left(\mathrm{tan}x+1\right)=0$
Now,
$\mathrm{tan}x-4=0$ or $\mathrm{tan}x+1=0$
$\mathrm{tan}x=4$ $\mathrm{tan}x=-1$
$x=\mathrm{arctan}\left(4\right)$ $x=\mathrm{arctan}\left(-1\right)$
$x=\eta \pi +\mathrm{arctan}\left(4\right)$ or $x=\eta \pi -\frac{\pi }{4}$
Jeffrey Jordon