3/4n+5=2/3n

Solution for 3/4n+5=2/3n equation:

3/4n+5=2/3n

We move all terms to the left:

3/4n+5-(2/3n)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

3/4n-(+2/3n)+5=0

We get rid of parentheses

3/4n-2/3n+5=0

We calculate fractions


9n/12n^2+(-8n)/12n^2+5=0

We multiply all the terms by the denominator


9n+(-8n)+5*12n^2=0

Wy multiply elements

60n^2+9n+(-8n)=0

We get rid of parentheses

60n^2+9n-8n=0

We add all the numbers together, and all the variables

60n^2+n=0

a = 60; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·60·0
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*60}=\frac{-2}{120}
=-1/60
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*60}=\frac{0}{120}
=0
$