1/5n+13=n-107

Solution for 1/5n+13=n-107 equation:

1/5n+13=n-107

We move all terms to the left:

1/5n+13-(n-107)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We get rid of parentheses

1/5n-n+107+13=0

We multiply all the terms by the denominator


-n*5n+107*5n+13*5n+1=0

Wy multiply elements

-5n^2+535n+65n+1=0

We add all the numbers together, and all the variables

-5n^2+600n+1=0

a = -5; b = 600; c = +1;
Δ = b2-4ac
Δ = 6002-4·(-5)·1
Δ = 360020
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:

$\sqrt{\Delta}=\sqrt{360020}=\sqrt{4*90005}=\sqrt{4}*\sqrt{90005}=2\sqrt{90005}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(600)-2\sqrt{90005}}{2*-5}=\frac{-600-2\sqrt{90005}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(600)+2\sqrt{90005}}{2*-5}=\frac{-600+2\sqrt{90005}}{-10}
$