1/226n-13=13n

Solution for 1/226n-13=13n equation:

1/226n-13=13n

We move all terms to the left:

1/226n-13-(13n)=0


Domain of the equation: 226n!=0

n!=0/226

n!=0

n∈R


We add all the numbers together, and all the variables

-13n+1/226n-13=0

We multiply all the terms by the denominator


-13n*226n-13*226n+1=0

Wy multiply elements

-2938n^2-2938n+1=0

a = -2938; b = -2938; c = +1;
Δ = b2-4ac
Δ = -29382-4·(-2938)·1
Δ = 8643596
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8643596}=\sqrt{4*2160899}=\sqrt{4}*\sqrt{2160899}=2\sqrt{2160899}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2938)-2\sqrt{2160899}}{2*-2938}=\frac{2938-2\sqrt{2160899}}{-5876}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2938)+2\sqrt{2160899}}{2*-2938}=\frac{2938+2\sqrt{2160899}}{-5876}
$