4/2n-7=20/6n+5

Solution for 4/2n-7=20/6n+5 equation:

4/2n-7=20/6n+5

We move all terms to the left:

4/2n-7-(20/6n+5)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 6n+5)!=0

n∈R


We get rid of parentheses

4/2n-20/6n-5-7=0

We calculate fractions


24n/12n^2+(-40n)/12n^2-5-7=0

We add all the numbers together, and all the variables

24n/12n^2+(-40n)/12n^2-12=0

We multiply all the terms by the denominator


24n+(-40n)-12*12n^2=0

Wy multiply elements

-144n^2+24n+(-40n)=0

We get rid of parentheses

-144n^2+24n-40n=0

We add all the numbers together, and all the variables

-144n^2-16n=0

a = -144; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-144)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-144}=\frac{0}{-288}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-144}=\frac{32}{-288}
=-1/9
$