52x+2+16∗15x−9x+1=0{\displaystyle 5^{2x+2}+16*15^{x}-9^{x+1}=0}
52x+2+16∗15x−9x+1=052x∗52+16∗5x∗3x−32x∗32=052x32x+16∗5x3x−9=0t=5x3x2t2+16t−9=0−16±162+4∗9∗252∗25−16±3450t1=1850 t2=−15x3x=1850 5x3x=−15x3x=32∗252∗2 x=wrongvalue5x3x=32525x∗3−x=32∗5−2x=−2 x=−2{\displaystyle {\begin{aligned}5^{2x+2}+16*15^{x}-9^{x+1}=0\\5^{2x}*5^{2}+16*5^{x}*3^{x}-3^{2x}*3^{2}=0\\{\frac {5^{2x}}{3^{2x}}}+16*{\frac {5^{x}}{3^{x}}}-9=0\\t={\frac {5^{x}}{3^{x}}}\\2t^{2}+16t-9=0\\{\frac {-16\pm {\sqrt {16^{2}+4*9*25}}}{2*25}}\\{\frac {-16\pm 34}{50}}\\t_{1}={\frac {18}{50}}\ \ \ \ t_{2}=-1\\{\frac {5^{x}}{3^{x}}}={\frac {18}{50}}\ \ \ \ \ \ {\frac {5^{x}}{3^{x}}}=-1\\{\frac {5^{x}}{3^{x}}}={\frac {3^{2}*2}{5^{2}*2}}\ \ \ \ \ \ \ x=wrongvalue\\{\frac {5^{x}}{3^{x}}}={\frac {3^{2}}{5^{2}}}\\5^{x}*3^{-x}=3^{2}*5^{-2}\\x=-2\ \ \ x=-2\end{aligned}}}