-5/9n=98-n

Solution for -5/9n=98-n equation:

-5/9n=98-n

We move all terms to the left:

-5/9n-(98-n)=0


Domain of the equation: 9n!=0

n!=0/9

n!=0

n∈R


We add all the numbers together, and all the variables

-5/9n-(-1n+98)=0

We get rid of parentheses

-5/9n+1n-98=0

We multiply all the terms by the denominator


1n*9n-98*9n-5=0

Wy multiply elements

9n^2-882n-5=0

a = 9; b = -882; c = -5;
Δ = b2-4ac
Δ = -8822-4·9·(-5)
Δ = 778104
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:

$\sqrt{\Delta}=\sqrt{778104}=\sqrt{36*21614}=\sqrt{36}*\sqrt{21614}=6\sqrt{21614}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-882)-6\sqrt{21614}}{2*9}=\frac{882-6\sqrt{21614}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-882)+6\sqrt{21614}}{2*9}=\frac{882+6\sqrt{21614}}{18}
$