2x/2^2x=8

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

2x/2^2x=8

We move all terms to the left:

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


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

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


2x-8*2^2x=0

Wy multiply elements

-16x^2+2x=0

a = -16; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-16)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-16}=\frac{-4}{-32}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-16}=\frac{0}{-32}
=0
$