8^2m+2^2m=1/4

Solution for 8^2m+2^2m=1/4 equation:

8^2m+2^2m=1/4

We move all terms to the left:

8^2m+2^2m-(1/4)=0

We add all the numbers together, and all the variables

8^2m+2^2m-(+1/4)=0

We get rid of parentheses

8^2m+2^2m-1/4=0

We multiply all the terms by the denominator


8^2m*4+2^2m*4-1=0

Wy multiply elements

32m^2+8m^2-1=0

We add all the numbers together, and all the variables

40m^2-1=0

a = 40; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·40·(-1)
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*40}=\frac{0-4\sqrt{10}}{80}
=-\frac{4\sqrt{10}}{80}
=-\frac{\sqrt{10}}{20}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*40}=\frac{0+4\sqrt{10}}{80}
=\frac{4\sqrt{10}}{80}
=\frac{\sqrt{10}}{20}
$