9/5n=15-2n

Solution for 9/5n=15-2n equation:

9/5n=15-2n

We move all terms to the left:

9/5n-(15-2n)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

9/5n-(-2n+15)=0

We get rid of parentheses

9/5n+2n-15=0

We multiply all the terms by the denominator


2n*5n-15*5n+9=0

Wy multiply elements

10n^2-75n+9=0

a = 10; b = -75; c = +9;
Δ = b2-4ac
Δ = -752-4·10·9
Δ = 5265
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:

$\sqrt{\Delta}=\sqrt{5265}=\sqrt{81*65}=\sqrt{81}*\sqrt{65}=9\sqrt{65}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-9\sqrt{65}}{2*10}=\frac{75-9\sqrt{65}}{20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+9\sqrt{65}}{2*10}=\frac{75+9\sqrt{65}}{20}
$