(11n+5)13n=n

Solution for (11n+5)13n=n equation:

(11n+5)13n=n

We move all terms to the left:

(11n+5)13n-(n)=0

We add all the numbers together, and all the variables

-1n+(11n+5)13n=0

We multiply parentheses

143n^2-1n+65n=0

We add all the numbers together, and all the variables

143n^2+64n=0

a = 143; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·143·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*143}=\frac{-128}{286}
=-64/143
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*143}=\frac{0}{286}
=0
$