-5/3n-1/4n=1

Solution for -5/3n-1/4n=1 equation:

-5/3n-1/4n=1

We move all terms to the left:

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


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We calculate fractions


(-20n)/12n^2+(-3n)/12n^2-1=0

We multiply all the terms by the denominator


(-20n)+(-3n)-1*12n^2=0

Wy multiply elements

-12n^2+(-20n)+(-3n)=0

We get rid of parentheses

-12n^2-20n-3n=0

We add all the numbers together, and all the variables

-12n^2-23n=0

a = -12; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·(-12)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*-12}=\frac{0}{-24}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*-12}=\frac{46}{-24}
=-1+11/12
$