21/3+3n=4/5n

Solution for 21/3+3n=4/5n equation:

21/3+3n=4/5n

We move all terms to the left:

21/3+3n-(4/5n)=0


Domain of the equation: 5n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

3n-(+4/5n)+21/3=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

3n-4/5n+7=0

We multiply all the terms by the denominator


3n*5n+7*5n-4=0

Wy multiply elements

15n^2+35n-4=0

a = 15; b = 35; c = -4;
Δ = b2-4ac
Δ = 352-4·15·(-4)
Δ = 1465
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-\sqrt{1465}}{2*15}=\frac{-35-\sqrt{1465}}{30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1465}}{2*15}=\frac{-35+\sqrt{1465}}{30}
$