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

We add all the numbers together, and all the variables

17n+16*12n^2=0

Wy multiply elements

192n^2+17n=0

a = 192; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·192·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*192}=\frac{-34}{384}
=-17/192
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*192}=\frac{0}{384}
=0
$