-1/3х²+3 = х²+3х
<span>-1/3х²+3 - х²-3х = 0
</span>-1 1/3х²-3х+3 = 0
4\3х²+3х-3 = 0
D = 9+4*4/3*3 = 144 (12)
х1 = (-3+12):8/3 = 9*3/8
х1 = 27/8 = 3 3/8
х2 = (-3-12)*3/8 = -15*3/8
х2 = -45/8 = -5 5/8
![(\frac{1}{3})^{5x^2+8x-4}<1](https://tex.z-dn.net/?f=+%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B5x%5E2%2B8x-4%7D%3C1++)
![(\frac{1}{3})^{5x^2+8x-4}<(\frac{1}{3})^0](https://tex.z-dn.net/?f=+%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B5x%5E2%2B8x-4%7D%3C%28%5Cfrac%7B1%7D%7B3%7D%29%5E0++)
![5x^2+8x-4>0](https://tex.z-dn.net/?f=+5x%5E2%2B8x-4%3E0++)
![5x^2+8x-4=0](https://tex.z-dn.net/?f=+5x%5E2%2B8x-4%3D0++)
![D=8^2-4*5*(-4)=64+80=144](https://tex.z-dn.net/?f=+D%3D8%5E2-4%2A5%2A%28-4%29%3D64%2B80%3D144+)
![x_1=\frac{-8+12}{10}=0.4](https://tex.z-dn.net/?f=+x_1%3D%5Cfrac%7B-8%2B12%7D%7B10%7D%3D0.4++)
![x_2=\frac{-8-12}{10}=-2](https://tex.z-dn.net/?f=+x_2%3D%5Cfrac%7B-8-12%7D%7B10%7D%3D-2+)
![5(x-0.4)(x+2)>0](https://tex.z-dn.net/?f=+5%28x-0.4%29%28x%2B2%29%3E0+)
-/////////////-(-2)-------- - -------(0.4)-/////////////-
Ответ:
∞
∪
∞ ![)](https://tex.z-dn.net/?f=+%29+)
3x-15>0
x-5>0
x>5
x принадлежит промежутку от 5 до плюс бесконечности, не включая 5