-3^(-x)-6=-3^x+10Solve the equation below for x by graphing plz

to graph it, just graph [tex]y=-3^{-x}-6[/tex] and [tex]y=-3^x+10[/tex] and see where they intersect

I would like to solve it by using math and not graphing
if you don't want to see the math, just don't scroll down
the graphical meathod is above, first line, just read it

hmm
multiply both sides by -1
[tex]3^{-x}+6=3^x-10[/tex]
multiply both sides by [tex]3^x[/tex]
[tex]3^0+6(3^x)=3^{2x}-10(3^x)[/tex]
[tex]1+6(3^x)=3^{2x}-10(3^x)[/tex]
minus 1 from both sides and minus 6(3^x) from both sides
[tex]0=3^{2x}-16(3^x)-1[/tex]
use u subsitution
[tex]u=3^x[/tex]
we can rewrite it as
[tex]0=u^2-16u-1[/tex]
now factor
I mean use quadratic formula
for [tex]ax^2+bx+c=0[/tex] [tex]x=\frac{-b+/-\sqrt{b^2-4ac}}{2a}[/tex]
so for 0=u^2-16u-1, a=1, b=-16, c=-1
[tex]u=\frac{-(-16)+/-\sqrt{(-16)^2-4(1)(-1)}{2(1)}[/tex]
[tex]u=8+/-\sqrt{65}[/tex]
remember that u=3^x so u>0
if we have u=8+√65, it's fine, but u=8-√65 is negative and not allowed
so therfor
[tex]u=8+\sqrt{65}=3^x[/tex]
[tex]8+\sqrt{65}=3^x[/tex]
if you take the log base 3 of both sides you get
[tex]log_3(8+\sqrt{65})=x[/tex]
if you use ln then
[tex]ln(8+\sqrt{65})=xln(3)[/tex]
then
[tex]\frac{ln(8+\sqrt{65})}{ln(3)}=x[/tex]