3/4n=1/3n+10

Solution for 3/4n=1/3n+10 equation:

3/4n=1/3n+10

We move all terms to the left:

3/4n-(1/3n+10)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 3n+10)!=0

n∈R


We get rid of parentheses

3/4n-1/3n-10=0

We calculate fractions


9n/12n^2+(-4n)/12n^2-10=0

We multiply all the terms by the denominator


9n+(-4n)-10*12n^2=0

Wy multiply elements

-120n^2+9n+(-4n)=0

We get rid of parentheses

-120n^2+9n-4n=0

We add all the numbers together, and all the variables

-120n^2+5n=0

a = -120; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-120)·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*-120}=\frac{-10}{-240}
=1/24
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-120}=\frac{0}{-240}
=0
$