Question

Solve

3^2x + 3^x - 21

check extraneous roots

Answer 1

Is the first term 3^2x (which is 9x) or 3 x^2 or 3^(2x)?

You have not stated an equation, only a function definition or "expression". There is nothing to "solve"

The solution to
3^(2x) + 3^x -21 = 0 is about x = 1.29

Answer 2

how was it solved ? quad formula. what is a b and c?

Answer 3

If you are talking about using a quadratic formula, you wrote the equation wrong. As i said before, you did not even write and equation

It should have been 3x^2 + 3x -21 = 0, whic is the same as x^2 +x -7 = 0
That equation has only irrational roots.

I solved the other equation by trial and error.

Answer 4

Here is a way to solve
3^(2x) + 3^x -21 = 0
Let 3^x = y
Then,
y^2 + y -21 = 0
b^2 -4ac = 85
The roots are:
y = [-1 +/- sqrt 85]/2
= -5.1098 or 4.1098
When y = 4.1098,
x = (lny)/ln3 = 1.2865
I mentioned that solution in a previous post.

There is another "y" solution corresponding to y = -5.1098
However that appears to require the log of a negative number, which has no real solution for x.