4/n-9=-9+1+2n+12

Solution for 4/n-9=-9+1+2n+12 equation:

4/n-9=-9+1+2n+12

We move all terms to the left:

4/n-9-(-9+1+2n+12)=0


Domain of the equation: n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-13n-2n*n+4=0

Wy multiply elements

-2n^2-13n+4=0

a = -2; b = -13; c = +4;
Δ = b2-4ac
Δ = -132-4·(-2)·4
Δ = 201
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{-(-13)-\sqrt{201}}{2*-2}=\frac{13-\sqrt{201}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{201}}{2*-2}=\frac{13+\sqrt{201}}{-4}
$