Подставляем значения: (0.2)^2 - (-5)/0,2=0,04 +5*2=10,04
По порядку действия
1)4,3+7,9=12,2
2)12,2-2,3=9,9
3)9,9+2,1=12
![3\sin^2x+\sin x\cos x=2\cos^2x\\ \\ 3\sin^2x+\sin x\cos x-2\cos^2x=0](https://tex.z-dn.net/?f=3%5Csin%5E2x%2B%5Csin+x%5Ccos+x%3D2%5Ccos%5E2x%5C%5C+%5C%5C+3%5Csin%5E2x%2B%5Csin+x%5Ccos+x-2%5Ccos%5E2x%3D0)
Это однородное уравнение, разделим обе части уравнения на cos²x≠0
![\displaystyle \frac{3\sin^2x}{\cos^2x}+\frac{\sin x\cos x}{\cos^2 x}-\frac{2\cos^2x}{\cos^2x}=0\\ \\ \frac{3\sin^2x}{\cos^2x}+\frac{\sin x}{\cos x}-2=0](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Cfrac%7B3%5Csin%5E2x%7D%7B%5Ccos%5E2x%7D%2B%5Cfrac%7B%5Csin+x%5Ccos+x%7D%7B%5Ccos%5E2+x%7D-%5Cfrac%7B2%5Ccos%5E2x%7D%7B%5Ccos%5E2x%7D%3D0%5C%5C+%5C%5C+%5Cfrac%7B3%5Csin%5E2x%7D%7B%5Ccos%5E2x%7D%2B%5Cfrac%7B%5Csin+x%7D%7B%5Ccos+x%7D-2%3D0)
Известно, что отношение sinx/cosx равно tgx, получим
![\tt 3tg^2x+tgx-2=0](https://tex.z-dn.net/?f=%5Ctt+3tg%5E2x%2Btgx-2%3D0)
Пусть
, получим квадратное уравнение относительно t
![3t^2+t-2=0](https://tex.z-dn.net/?f=3t%5E2%2Bt-2%3D0)
![D=b^2-4ac=1^2-4\cdot3\cdot(-2)=1+24=25\\ \\ t_1=\dfrac{-b+\sqrt{D}}{2a}=\dfrac{-1+5}{2\cdot3}=\dfrac{4}{2\cdot3}=\dfrac{2}{3};\\ \\ t_2=\dfrac{-b-\sqrt{D}}{2a}=\dfrac{-1-5}{2\cdot3}=-\dfrac{6}{2\cdot3}=-1](https://tex.z-dn.net/?f=D%3Db%5E2-4ac%3D1%5E2-4%5Ccdot3%5Ccdot%28-2%29%3D1%2B24%3D25%5C%5C+%5C%5C+t_1%3D%5Cdfrac%7B-b%2B%5Csqrt%7BD%7D%7D%7B2a%7D%3D%5Cdfrac%7B-1%2B5%7D%7B2%5Ccdot3%7D%3D%5Cdfrac%7B4%7D%7B2%5Ccdot3%7D%3D%5Cdfrac%7B2%7D%7B3%7D%3B%5C%5C+%5C%5C+t_2%3D%5Cdfrac%7B-b-%5Csqrt%7BD%7D%7D%7B2a%7D%3D%5Cdfrac%7B-1-5%7D%7B2%5Ccdot3%7D%3D-%5Cdfrac%7B6%7D%7B2%5Ccdot3%7D%3D-1)
Возвращаемся к обратной замене
![tgx=\dfrac{2}{3}~~~~\Rightarrow~~~~ \boxed{x=\tt{arctg}\dfrac{2}{3}+\pi n,n \in \mathbb{Z}}](https://tex.z-dn.net/?f=tgx%3D%5Cdfrac%7B2%7D%7B3%7D~~~~%5CRightarrow~~~~+%5Cboxed%7Bx%3D%5Ctt%7Barctg%7D%5Cdfrac%7B2%7D%7B3%7D%2B%5Cpi+n%2Cn+%5Cin+%5Cmathbb%7BZ%7D%7D)
![\tt tgx=-1~~~~\Rightarrow~~~ \boxed{x=-\frac{\pi}{4}+\pi n,n \in \mathbb{Z}}](https://tex.z-dn.net/?f=%5Ctt+tgx%3D-1~~~~%5CRightarrow~~~+%5Cboxed%7Bx%3D-%5Cfrac%7B%5Cpi%7D%7B4%7D%2B%5Cpi+n%2Cn+%5Cin+%5Cmathbb%7BZ%7D%7D)
Решение задания приложено