-2/3n+5=20-n

Solution for -2/3n+5=20-n equation:

-2/3n+5=20-n

We move all terms to the left:

-2/3n+5-(20-n)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

-2/3n-(-1n+20)+5=0

We get rid of parentheses

-2/3n+1n-20+5=0

We multiply all the terms by the denominator


1n*3n-20*3n+5*3n-2=0

Wy multiply elements

3n^2-60n+15n-2=0

We add all the numbers together, and all the variables

3n^2-45n-2=0

a = 3; b = -45; c = -2;
Δ = b2-4ac
Δ = -452-4·3·(-2)
Δ = 2049
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{2049}}{2*3}=\frac{45-\sqrt{2049}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2049}}{2*3}=\frac{45+\sqrt{2049}}{6}
$