solve the equation 3^2x + 2.3^x - 15 = 0

Answer 1

did you mean ...

3^(2x) + 2(3^x) - 15 = 0 ?

I will assume you did.

let 3^x = t
your equation becomes
t^2 + 2t - 15 = 0
(t+5)(t-3) = 0
t = -5 or t = 3

then 3^x = -5, which has no solution or
3^x = 3
x = 1