x/12^x=127(6)^x

Solution for x/12^x=127(6)^x equation:

x/12^x=127(6)^x

We move all terms to the left:

x/12^x-(127(6)^x)=0


Domain of the equation: 12^x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
x/12^x-1276^x=0

We multiply all the terms by the denominator


x-1276^x*12^x=0

Wy multiply elements

-15312x^2+x=0

a = -15312; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-15312)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-15312}=\frac{-2}{-30624}
=1/15312
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-15312}=\frac{0}{-30624}
=0
$