2/13n=-8+n

Solution for 2/13n=-8+n equation:

2/13n=-8+n

We move all terms to the left:

2/13n-(-8+n)=0


Domain of the equation: 13n!=0

n!=0/13

n!=0

n∈R


We add all the numbers together, and all the variables

2/13n-(n-8)=0

We get rid of parentheses

2/13n-n+8=0

We multiply all the terms by the denominator


-n*13n+8*13n+2=0

Wy multiply elements

-13n^2+104n+2=0

a = -13; b = 104; c = +2;
Δ = b2-4ac
Δ = 1042-4·(-13)·2
Δ = 10920
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:

$\sqrt{\Delta}=\sqrt{10920}=\sqrt{4*2730}=\sqrt{4}*\sqrt{2730}=2\sqrt{2730}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(104)-2\sqrt{2730}}{2*-13}=\frac{-104-2\sqrt{2730}}{-26}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(104)+2\sqrt{2730}}{2*-13}=\frac{-104+2\sqrt{2730}}{-26}
$