Solve cos^2x-sinxcosx-2sin^2x-m=0

$$\cos ^ { 2 } x - \sin x \cos x - 2 \sin ^ { 2 } x - m = 0$$

Solve for m (complex solution)

$$m=\left(\frac{3}{4}+\frac{1}{4}i\right)e^{2ix}+\left(\frac{3}{4}-\frac{1}{4}i\right)e^{-2ix}-\frac{1}{2}$$

Solve for x (complex solution)

$$x=\left(-\frac{1}{2}i\right)\ln(10)+\left(-i\right)\ln(\left(-\frac{1}{10}\right)\left(\left(6-2i\right)m+\left(3-i\right)+\left(3-i\right)\left(4m^{2}+4m-9\right)^{\frac{1}{2}}\right)^{\frac{1}{2}})+2\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$x=i\ln(10)+\left(-\frac{1}{2}i\right)\ln(\left(60-20i\right)m+\left(30-10i\right)+\left(30-10i\right)\left(4m^{2}+4m-9\right)^{\frac{1}{2}})+2n_{2}\pi \text{, }n_{2}\in \mathrm{Z}$$

$$x=i\ln(10)+\left(-\frac{1}{2}i\right)\ln(\left(60-20i\right)m+\left(30-10i\right)+\left(-30+10i\right)\left(4m^{2}+4m-9\right)^{\frac{1}{2}})+2n_{3}\pi \text{, }n_{3}\in \mathrm{Z}$$

$$x=\left(-\frac{1}{2}i\right)\ln(10)+\left(-i\right)\ln(\left(-\frac{1}{10}\right)\left(\left(6-2i\right)m+\left(3-i\right)+\left(-3+i\right)\left(4m^{2}+4m-9\right)^{\frac{1}{2}}\right)^{\frac{1}{2}})+2\pi n_{4}\text{, }n_{4}\in \mathrm{Z}$$

Solve for m

$$m=\frac{2\left(\cos(x)\right)^{2}-4\left(\sin(x)\right)^{2}-\sin(2x)}{2}$$