6n/3n-7=3/2n+5

Solution for 6n/3n-7=3/2n+5 equation:

6n/3n-7=3/2n+5

We move all terms to the left:

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


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 2n+5)!=0

n∈R


We get rid of parentheses

6n/3n-3/2n-5-7=0

We calculate fractions


12n^2/6n^2+(-9n)/6n^2-5-7=0

We add all the numbers together, and all the variables

12n^2/6n^2+(-9n)/6n^2-12=0

We multiply all the terms by the denominator


12n^2+(-9n)-12*6n^2=0

Wy multiply elements

12n^2-72n^2+(-9n)=0

We get rid of parentheses

12n^2-72n^2-9n=0

We add all the numbers together, and all the variables

-60n^2-9n=0

a = -60; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-60)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-60}=\frac{0}{-120}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-60}=\frac{18}{-120}
=-3/20
$