3/4n+7=1/3n-2

Solution for 3/4n+7=1/3n-2 equation:

3/4n+7=1/3n-2

We move all terms to the left:

3/4n+7-(1/3n-2)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 3n-2)!=0

n∈R


We get rid of parentheses

3/4n-1/3n+2+7=0

We calculate fractions


9n/12n^2+(-4n)/12n^2+2+7=0

We add all the numbers together, and all the variables

9n/12n^2+(-4n)/12n^2+9=0

We multiply all the terms by the denominator


9n+(-4n)+9*12n^2=0

Wy multiply elements

108n^2+9n+(-4n)=0

We get rid of parentheses

108n^2+9n-4n=0

We add all the numbers together, and all the variables

108n^2+5n=0

a = 108; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·108·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*108}=\frac{-10}{216}
=-5/108
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*108}=\frac{0}{216}
=0
$