Math help needed

WHY DON'T WRITE IT AS SUCH?!!!!!!!!!!!!!!!!. You mean:

2^x + 2^-x=6???????????????????????????

Solve for x over the real numbers:
2^(-x)+2^x = 6

Simplify and substitute y = 2^x:
2^(-x)+2^x  =  1/2^x+2^x  =  y+1/y  =  6:
y+1/y = 6

Bring y+1/y together using the common denominator y:
(y^2+1)/y = 6

Multiply both sides by y:
y^2+1 = 6 y

Subtract 6 y from both sides:
y^2-6 y+1 = 0

Subtract 1 from both sides:
y^2-6 y = -1

Add 9 to both sides:
y^2-6 y+9 = 8

Write the left hand side as a square:
(y-3)^2 = 8

Take the square root of both sides:
y-3 = 2 sqrt(2) or y-3 = -2 sqrt(2)

Add 3 to both sides:
y = 3+2 sqrt(2) or y-3 = -2 sqrt(2)

Substitute back for y = 2^x:
2^x = 3+2 sqrt(2) or y-3 = -2 sqrt(2)

Take the logarithm base 2 of both sides:
x = (log(3+2 sqrt(2)))/(log(2)) or y-3 = -2 sqrt(2)

Add 3 to both sides:
x = (log(3+2 sqrt(2)))/(log(2)) or y = 3-2 sqrt(2)

Substitute back for y = 2^x:
x = (log(3+2 sqrt(2)))/(log(2)) or 2^x = 3-2 sqrt(2)

Take the logarithm base 2 of both sides:
Answer: | 
| x = (log(3+2 sqrt(2)))/(log(2))                               or x = (log(3-2 sqrt(2)))/(log(2))

2x + 2 - x=6

x=6 - 2

x=4

The equation deals with variables as exponents. Thank you for trying to help, though.

2^x + 2^(-x)  = 6  rewrite as

2^x +  1 / [2^x)  = 6        multiply through by  2^x

[2^x][2^x] + 1  = 6[2^x]    subtract 6[2^x]  from both sides

[2^x]^2 -+ 1 - 6[2^x]   = 0       let 2^x = a   ..... and we have.....

a^2  + 1 - 6a  = 0     rearrange

a^2 - 6a + 1 = 0

Using the quadratic formula to solve for a, we have  .......a = 3-2 sqrt(2)   or  a = 3 + 2sqrt(2)

Thus  a = 2^x

And we have that

2^x = 3 - sqrt(2)         take the log of both sides

log2^x   = log [3 -2 sqrt(2) ]     and by a log property, we can write

x*log(2)  = log[ 3 - 2sqrt(2)]   divide both sides by log(2)

x = log[3 - 2sqrt(2)] / log(2)  = about -2.5431

In similar fashion, x also equals.....

 log[ 3 + 2sqrt(2)] / log(2)  = about 2.5431

Here's a graph of  both sides of this strange equation  with the intersection points being the solutions.....

https://www.desmos.com/calculator/uomirk7pas