how many answers do this equation have$3^{2x}-34(15^{x-1})+5^{2x}=0$ How many answers do this equation have?
$3^{2x}-34(15^{x-1})+5^{2x}=0$
My Attempt:$3^{2x}+5^{2x}=34(15^{x-1})$.Now what to do?

$$3^{2x}-34(15^{x-1})+5^{2x}=0$$
$$3^{2x}-\frac{34}{15}(15^{x})+5^{2x}=0$$
$$15\cdot3^{2x}-34\cdot 3^x \cdot 5^x+15\cdot5^{2x}=0$$
$$15\cdot\left(\frac{3}{5}\right)^{2x}-34\cdot \left(\frac{3}{5}\right)^{x}+15=0$$
$\left(\frac{3}{5}\right)^{x}=t$
$$15\cdot t^{2}-34\cdot t+15=0$$
$t=\frac35$ or $t=\frac53$
$x=1$ or $x=-1$
