3/2n+1/3n=11/10

Solution for 3/2n+1/3n=11/10 equation:

3/2n+1/3n=11/10

We move all terms to the left:

3/2n+1/3n-(11/10)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

3/2n+1/3n-(+11/10)=0

We get rid of parentheses

3/2n+1/3n-11/10=0

We calculate fractions


(-198n^2)/60n^2+90n/60n^2+20n/60n^2=0

We multiply all the terms by the denominator


(-198n^2)+90n+20n=0

We add all the numbers together, and all the variables

(-198n^2)+110n=0

We get rid of parentheses

-198n^2+110n=0

a = -198; b = 110; c = 0;
Δ = b2-4ac
Δ = 1102-4·(-198)·0
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-110}{2*-198}=\frac{-220}{-396}
=5/9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+110}{2*-198}=\frac{0}{-396}
=0
$