8^x=64/2^x

Solution for 8^x=64/2^x equation:

8^x=64/2^x

We move all terms to the left:

8^x-(64/2^x)=0


Domain of the equation: 2^x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

8^x-64/2^x=0

We multiply all the terms by the denominator


8^x*2^x-64=0

Wy multiply elements

16x^2-64=0

a = 16; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·16·(-64)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64}{2*16}=\frac{-64}{32}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64}{2*16}=\frac{64}{32}
=2
$