1/5n+4/3n=2

Solution for 1/5n+4/3n=2 equation:

1/5n+4/3n=2

We move all terms to the left:

1/5n+4/3n-(2)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We calculate fractions


3n/15n^2+20n/15n^2-2=0

We multiply all the terms by the denominator


3n+20n-2*15n^2=0

We add all the numbers together, and all the variables

23n-2*15n^2=0

Wy multiply elements

-30n^2+23n=0

a = -30; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-30)·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*-30}=\frac{-46}{-60}
=23/30
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-30}=\frac{0}{-60}
=0
$