2/5n=10+n

Solution for 2/5n=10+n equation:

2/5n=10+n

We move all terms to the left:

2/5n-(10+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

2/5n-(n+10)=0

We get rid of parentheses

2/5n-n-10=0

We multiply all the terms by the denominator


-n*5n-10*5n+2=0

Wy multiply elements

-5n^2-50n+2=0

a = -5; b = -50; c = +2;
Δ = b2-4ac
Δ = -502-4·(-5)·2
Δ = 2540
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:

$\sqrt{\Delta}=\sqrt{2540}=\sqrt{4*635}=\sqrt{4}*\sqrt{635}=2\sqrt{635}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{635}}{2*-5}=\frac{50-2\sqrt{635}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{635}}{2*-5}=\frac{50+2\sqrt{635}}{-10}
$