5 2 x + 2 + 16 ∗ 15 x − 9 x + 1 = 0 {\displaystyle 5^{2x+2}+16*15^{x}-9^{x+1}=0}
5 2 x + 2 + 16 ∗ 15 x − 9 x + 1 = 0 5 2 x ∗ 5 2 + 16 ∗ 5 x ∗ 3 x − 3 2 x ∗ 3 2 = 0 5 2 x 3 2 x + 16 ∗ 5 x 3 x − 9 = 0 t = 5 x 3 x 2 t 2 + 16 t − 9 = 0 − 16 ± 16 2 + 4 ∗ 9 ∗ 25 2 ∗ 25 − 16 ± 34 50 t 1 = 18 50 t 2 = − 1 5 x 3 x = 18 50 5 x 3 x = − 1 5 x 3 x = 3 2 ∗ 2 5 2 ∗ 2 x = w r o n g v a l u e 5 x 3 x = 3 2 5 2 5 x ∗ 3 − x = 3 2 ∗ 5 − 2 x = − 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}}}
