1/2n+10=n-8

Solution for 1/2n+10=n-8 equation:

1/2n+10=n-8

We move all terms to the left:

1/2n+10-(n-8)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We get rid of parentheses

1/2n-n+8+10=0

We multiply all the terms by the denominator


-n*2n+8*2n+10*2n+1=0

Wy multiply elements

-2n^2+16n+20n+1=0

We add all the numbers together, and all the variables

-2n^2+36n+1=0

a = -2; b = 36; c = +1;
Δ = b2-4ac
Δ = 362-4·(-2)·1
Δ = 1304
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:

$\sqrt{\Delta}=\sqrt{1304}=\sqrt{4*326}=\sqrt{4}*\sqrt{326}=2\sqrt{326}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{326}}{2*-2}=\frac{-36-2\sqrt{326}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{326}}{2*-2}=\frac{-36+2\sqrt{326}}{-4}
$