T1/8^2x=4^12

Solution for T1/8^2x=4^12 equation:

1/8^2T=4^12

We move all terms to the left:

1/8^2T-(4^12)=0


Domain of the equation: 8^2T!=0

T!=0/1

T!=0

T∈R


We add all the numbers together, and all the variables

1/8^2T-16777216=0

We multiply all the terms by the denominator


-16777216*8^2T+1=0

Wy multiply elements

-134217728T^2+1=0

a = -134217728; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-134217728)·1
Δ = 536870912
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{536870912}=\sqrt{268435456*2}=\sqrt{268435456}*\sqrt{2}=16384\sqrt{2}$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16384\sqrt{2}}{2*-134217728}=\frac{0-16384\sqrt{2}}{-268435456}
=-\frac{16384\sqrt{2}}{-268435456}
=-\frac{\sqrt{2}}{-16384}
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16384\sqrt{2}}{2*-134217728}=\frac{0+16384\sqrt{2}}{-268435456}
=\frac{16384\sqrt{2}}{-268435456}
=\frac{\sqrt{2}}{-16384}
$