3/5n=2+n

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

3/5n=2+n

We move all terms to the left:

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


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3/5n-n-2=0

We multiply all the terms by the denominator


-n*5n-2*5n+3=0

Wy multiply elements

-5n^2-10n+3=0

a = -5; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·(-5)·3
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{10}}{2*-5}=\frac{10-4\sqrt{10}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{10}}{2*-5}=\frac{10+4\sqrt{10}}{-10}
$