n-3/2n-2=-n

Solution for n-3/2n-2=-n equation:

n-3/2n-2=-n

We move all terms to the left:

n-3/2n-2-(-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

n-3/2n-(-1n)-2=0

We get rid of parentheses

n-3/2n+1n-2=0

We multiply all the terms by the denominator


n*2n+1n*2n-2*2n-3=0

Wy multiply elements

2n^2+2n^2-4n-3=0

We add all the numbers together, and all the variables

4n^2-4n-3=0

a = 4; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·4·(-3)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*4}=\frac{-4}{8}
=-1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*4}=\frac{12}{8}
=1+1/2
$