Question 980846
{{{9^x-3^x=-1}}}
{{{(3^2)^x-3^x=-1}}}
{{{(3^(2x))-3^x=-1}}}
{{{(3^x)^2-3^x=-1}}}
{{{(3^x)^2-3^x+1=0}}}


Pick an arbitrary new variable.
Let {{{p=3^x}}}, and rewrite the equation as
{{{p^2-p+1=0}}}


Now first solve this equation for p.


{{{p=(1+- sqrt(1^2-4*1*1))/2}}}  according to general solution of a quadratic equation.
{{{p=(1+- sqrt(-3))/2}}}

{{{p=(1+- i*sqrt(3))/2}}}


Next substitute for p.
{{{3^x=(1+- i*sqrt(3))/2}}}, a complex result, still unfinished.
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Unless I made a mistake in the process, this is not a beginner's exercise.  Maybe another tutor can carry this to a solution for x.