n-8=1/2n+10

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

n-8=1/2n+10

We move all terms to the left:

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


Domain of the equation: 2n+10)!=0

n∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

2n^2-20n-16n-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}
$