2+n=15-7/8n

Solution for 2+n=15-7/8n equation:

2+n=15-7/8n

We move all terms to the left:

2+n-(15-7/8n)=0


Domain of the equation: 8n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

n-(-7/8n+15)+2=0

We get rid of parentheses

n+7/8n-15+2=0

We multiply all the terms by the denominator


n*8n-15*8n+2*8n+7=0

Wy multiply elements

8n^2-120n+16n+7=0

We add all the numbers together, and all the variables

8n^2-104n+7=0

a = 8; b = -104; c = +7;
Δ = b2-4ac
Δ = -1042-4·8·7
Δ = 10592
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:

$\sqrt{\Delta}=\sqrt{10592}=\sqrt{16*662}=\sqrt{16}*\sqrt{662}=4\sqrt{662}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-4\sqrt{662}}{2*8}=\frac{104-4\sqrt{662}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+4\sqrt{662}}{2*8}=\frac{104+4\sqrt{662}}{16}
$