5/2n-2=8+n

Solution for 5/2n-2=8+n equation:

5/2n-2=8+n

We move all terms to the left:

5/2n-2-(8+n)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

5/2n-(n+8)-2=0

We get rid of parentheses

5/2n-n-8-2=0

We multiply all the terms by the denominator


-n*2n-8*2n-2*2n+5=0

Wy multiply elements

-2n^2-16n-4n+5=0

We add all the numbers together, and all the variables

-2n^2-20n+5=0

a = -2; b = -20; c = +5;
Δ = b2-4ac
Δ = -202-4·(-2)·5
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{110}}{2*-2}=\frac{20-2\sqrt{110}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{110}}{2*-2}=\frac{20+2\sqrt{110}}{-4}
$