2/5n-9=n

Solution for 2/5n-9=n equation:

2/5n-9=n

We move all terms to the left:

2/5n-9-(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

-1n+2/5n-9=0

We multiply all the terms by the denominator


-1n*5n-9*5n+2=0

Wy multiply elements

-5n^2-45n+2=0

a = -5; b = -45; c = +2;
Δ = b2-4ac
Δ = -452-4·(-5)·2
Δ = 2065
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{-(-45)-\sqrt{2065}}{2*-5}=\frac{45-\sqrt{2065}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2065}}{2*-5}=\frac{45+\sqrt{2065}}{-10}
$