6/2n-5=2/n-7

Solution for 6/2n-5=2/n-7 equation:

6/2n-5=2/n-7

We move all terms to the left:

6/2n-5-(2/n-7)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: n-7)!=0

n∈R


We get rid of parentheses

6/2n-2/n+7-5=0

We calculate fractions


6n/2n^2+(-4n)/2n^2+7-5=0

We add all the numbers together, and all the variables

6n/2n^2+(-4n)/2n^2+2=0

We multiply all the terms by the denominator


6n+(-4n)+2*2n^2=0

Wy multiply elements

4n^2+6n+(-4n)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

4n^2+2n=0

a = 4; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·4·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*4}=\frac{-4}{8}
=-1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*4}=\frac{0}{8}
=0
$