1/3n+7/6=4/5n

Solution for 1/3n+7/6=4/5n equation:

1/3n+7/6=4/5n

We move all terms to the left:

1/3n+7/6-(4/5n)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 5n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

1/3n-(+4/5n)+7/6=0

We get rid of parentheses

1/3n-4/5n+7/6=0

We calculate fractions


525n^2/540n^2+180n/540n^2+(-432n)/540n^2=0

We multiply all the terms by the denominator


525n^2+180n+(-432n)=0

We get rid of parentheses

525n^2+180n-432n=0

We add all the numbers together, and all the variables

525n^2-252n=0

a = 525; b = -252; c = 0;
Δ = b2-4ac
Δ = -2522-4·525·0
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-252}{2*525}=\frac{0}{1050}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+252}{2*525}=\frac{504}{1050}
=12/25
$