1/2n+5=1/3n+7

Solution for 1/2n+5=1/3n+7 equation:

1/2n+5=1/3n+7

We move all terms to the left:

1/2n+5-(1/3n+7)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 3n+7)!=0

n∈R


We get rid of parentheses

1/2n-1/3n-7+5=0

We calculate fractions


3n/6n^2+(-2n)/6n^2-7+5=0

We add all the numbers together, and all the variables

3n/6n^2+(-2n)/6n^2-2=0

We multiply all the terms by the denominator


3n+(-2n)-2*6n^2=0

Wy multiply elements

-12n^2+3n+(-2n)=0

We get rid of parentheses

-12n^2+3n-2n=0

We add all the numbers together, and all the variables

-12n^2+n=0

a = -12; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-12)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-12}=\frac{-2}{-24}
=1/12
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-12}=\frac{0}{-24}
=0
$