2+2n=1/2n-3

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

2+2n=1/2n-3

We move all terms to the left:

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


Domain of the equation: 2n-3)!=0

n∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4n^2+6n+4n-1=0

We add all the numbers together, and all the variables

4n^2+10n-1=0

a = 4; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·4·(-1)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{29}}{2*4}=\frac{-10-2\sqrt{29}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{29}}{2*4}=\frac{-10+2\sqrt{29}}{8}
$