2/3n+7=3/4n-9

Solution for 2/3n+7=3/4n-9 equation:

2/3n+7=3/4n-9

We move all terms to the left:

2/3n+7-(3/4n-9)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 4n-9)!=0

n∈R


We get rid of parentheses

2/3n-3/4n+9+7=0

We calculate fractions


8n/12n^2+(-9n)/12n^2+9+7=0

We add all the numbers together, and all the variables

8n/12n^2+(-9n)/12n^2+16=0

We multiply all the terms by the denominator


8n+(-9n)+16*12n^2=0

Wy multiply elements

192n^2+8n+(-9n)=0

We get rid of parentheses

192n^2+8n-9n=0

We add all the numbers together, and all the variables

192n^2-1n=0

a = 192; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·192·0
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*192}=\frac{0}{384}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*192}=\frac{2}{384}
=1/192
$