n-9.00=3/5n

Solution for n-9.00=3/5n equation:

n-9.00=3/5n

We move all terms to the left:

n-9.00-(3/5n)=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-(+3/5n)-9.00=0

We add all the numbers together, and all the variables

n-(+3/5n)-9=0

We get rid of parentheses

n-3/5n-9=0

We multiply all the terms by the denominator


n*5n-9*5n-3=0

Wy multiply elements

5n^2-45n-3=0

a = 5; b = -45; c = -3;
Δ = b2-4ac
Δ = -452-4·5·(-3)
Δ = 2085
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{2085}}{2*5}=\frac{45-\sqrt{2085}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2085}}{2*5}=\frac{45+\sqrt{2085}}{10}
$