Solve the following equation:

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Solve the following equation:

Mathematics
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\[3^{2x+1} -26(3^x) - 9 = 0\] I have no idea where to start, could you please provide some hints? Thanks in advance!
do u want answer in terms of x or want to simplify it?
Let \(3^x = t\)

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as ganeshie said but before line up the variables so everything clear like this
\[-9-26 \times 3^{x}+3^{2x+1}=0\]
\[-9-26 \times 3^{x}+3(3^{x})^{2}\]
\[3t ^{2}-26t-9=0\]
then factorise it
@ayeshaafzal221 I believe I'm supposed to solve for X, I got the same equation you did, but my textbook says that the answer is 2?
yes the answer is 2
This is why math makes no sense... I read the equation, i caught on for the next part, then all that sht fell apart in my head
\[(t-9)(3t+1)=0\]
split this into two eq
\[t-9=0 , 3y+1=0\]
now from t-9=0 -> t=9
sub back the t value
\[3^{x}=9\]
English plz xD (I dont needa know this stuff I'm just looking at wat u guys r doing)
\[3^{2}=9\]
\[3^{x}=3^{2}\]
and for the other eq 3y-1=0 -> y=-1/3 has no solution
so x=2
ah yes of course, I'm so stupid. X.X - I forgot to convert the "t" back to the 3x^2
thats ok hope it helps :)
Thank's ayeshaa, I had some other problems with the same line of thought, I'll be able to solve them now. ;u;
Thank you! I'm closing the board now.

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