9+4/n=15-2n

Solution for 9+4/n=15-2n equation:

9+4/n=15-2n

We move all terms to the left:

9+4/n-(15-2n)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

4/n-(-2n+15)+9=0

We get rid of parentheses

4/n+2n-15+9=0

We multiply all the terms by the denominator


2n*n-15*n+9*n+4=0

We add all the numbers together, and all the variables

-6n+2n*n+4=0

Wy multiply elements

2n^2-6n+4=0

a = 2; b = -6; c = +4;
Δ = b2-4ac
Δ = -62-4·2·4
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2}{2*2}=\frac{4}{4}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2}{2*2}=\frac{8}{4}
=2
$