9-n=4/5n

Solution for 9-n=4/5n equation:

9-n=4/5n

We move all terms to the left:

9-n-(4/5n)=0


Domain of the equation: 5n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

-n-(+4/5n)+9=0

We add all the numbers together, and all the variables

-1n-(+4/5n)+9=0

We get rid of parentheses

-1n-4/5n+9=0

We multiply all the terms by the denominator


-1n*5n+9*5n-4=0

Wy multiply elements

-5n^2+45n-4=0

a = -5; b = 45; c = -4;
Δ = b2-4ac
Δ = 452-4·(-5)·(-4)
Δ = 1945
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{1945}}{2*-5}=\frac{-45-\sqrt{1945}}{-10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{1945}}{2*-5}=\frac{-45+\sqrt{1945}}{-10}
$