n=22/2n+9

Solution for n=22/2n+9 equation:

n=22/2n+9

We move all terms to the left:

n-(22/2n+9)=0


Domain of the equation: 2n+9)!=0

n∈R


We get rid of parentheses

n-22/2n-9=0

We multiply all the terms by the denominator


n*2n-9*2n-22=0

Wy multiply elements

2n^2-18n-22=0

a = 2; b = -18; c = -22;
Δ = b2-4ac
Δ = -182-4·2·(-22)
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-10\sqrt{5}}{2*2}=\frac{18-10\sqrt{5}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+10\sqrt{5}}{2*2}=\frac{18+10\sqrt{5}}{4}
$