2/5n=n+6

Solution for 2/5n=n+6 equation:

2/5n=n+6

We move all terms to the left:

2/5n-(n+6)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We get rid of parentheses

2/5n-n-6=0

We multiply all the terms by the denominator


-n*5n-6*5n+2=0

Wy multiply elements

-5n^2-30n+2=0

a = -5; b = -30; c = +2;
Δ = b2-4ac
Δ = -302-4·(-5)·2
Δ = 940
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:

$\sqrt{\Delta}=\sqrt{940}=\sqrt{4*235}=\sqrt{4}*\sqrt{235}=2\sqrt{235}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{235}}{2*-5}=\frac{30-2\sqrt{235}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{235}}{2*-5}=\frac{30+2\sqrt{235}}{-10}
$