1/5n+3=1/4n+2

Solution for 1/5n+3=1/4n+2 equation:

1/5n+3=1/4n+2

We move all terms to the left:

1/5n+3-(1/4n+2)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 4n+2)!=0

n∈R


We get rid of parentheses

1/5n-1/4n-2+3=0

We calculate fractions


4n/20n^2+(-5n)/20n^2-2+3=0

We add all the numbers together, and all the variables

4n/20n^2+(-5n)/20n^2+1=0

We multiply all the terms by the denominator


4n+(-5n)+1*20n^2=0

Wy multiply elements

20n^2+4n+(-5n)=0

We get rid of parentheses

20n^2+4n-5n=0

We add all the numbers together, and all the variables

20n^2-1n=0

a = 20; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·20·0
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*20}=\frac{0}{40}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*20}=\frac{2}{40}
=1/20
$