2a=64/2^a

Solution for 2a=64/2^a equation:

2a=64/2^a

We move all terms to the left:

2a-(64/2^a)=0


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

a!=0/1

a!=0

a∈R


We get rid of parentheses

2a-64/2^a=0

We multiply all the terms by the denominator


2a*2^a-64=0

Wy multiply elements

4a^2-64=0

a = 4; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·4·(-64)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32}{2*4}=\frac{-32}{8}
=-4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32}{2*4}=\frac{32}{8}
=4
$