1/2n-2-3=3-2n-3

Solution for 1/2n-2-3=3-2n-3 equation:

1/2n-2-3=3-2n-3

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

1/2n-(-2n)-5=0

We get rid of parentheses

1/2n+2n-5=0

We multiply all the terms by the denominator


2n*2n-5*2n+1=0

Wy multiply elements

4n^2-10n+1=0

a = 4; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·4·1
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{21}}{2*4}=\frac{10-2\sqrt{21}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{21}}{2*4}=\frac{10+2\sqrt{21}}{8}
$