1/5n+11=3/4n

Solution for 1/5n+11=3/4n equation:

1/5n+11=3/4n

We move all terms to the left:

1/5n+11-(3/4n)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 4n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

1/5n-(+3/4n)+11=0

We get rid of parentheses

1/5n-3/4n+11=0

We calculate fractions


4n/20n^2+(-15n)/20n^2+11=0

We multiply all the terms by the denominator


4n+(-15n)+11*20n^2=0

Wy multiply elements

220n^2+4n+(-15n)=0

We get rid of parentheses

220n^2+4n-15n=0

We add all the numbers together, and all the variables

220n^2-11n=0

a = 220; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·220·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*220}=\frac{0}{440}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*220}=\frac{22}{440}
=1/20
$