3/4n+1/6n=1

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

3/4n+1/6n=1

We move all terms to the left:

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


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R


We calculate fractions


18n/24n^2+4n/24n^2-1=0

We multiply all the terms by the denominator


18n+4n-1*24n^2=0

We add all the numbers together, and all the variables

22n-1*24n^2=0

Wy multiply elements

-24n^2+22n=0

a = -24; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-24)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-24}=\frac{-44}{-48}
=11/12
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-24}=\frac{0}{-48}
=0
$