2/3n+n=45

Solution for 2/3n+n=45 equation:

2/3n+n=45

We move all terms to the left:

2/3n+n-(45)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

n+2/3n-45=0

We multiply all the terms by the denominator


n*3n-45*3n+2=0

Wy multiply elements

3n^2-135n+2=0

a = 3; b = -135; c = +2;
Δ = b2-4ac
Δ = -1352-4·3·2
Δ = 18201
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{-(-135)-\sqrt{18201}}{2*3}=\frac{135-\sqrt{18201}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+\sqrt{18201}}{2*3}=\frac{135+\sqrt{18201}}{6}
$