13/5n-11/10n+11/3=7/6

Solution for 13/5n-11/10n+11/3=7/6 equation:

13/5n-11/10n+11/3=7/6

We move all terms to the left:

13/5n-11/10n+11/3-(7/6)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 10n!=0

n!=0/10

n!=0

n∈R


We add all the numbers together, and all the variables

13/5n-11/10n+11/3-(+7/6)=0

We get rid of parentheses

13/5n-11/10n+11/3-7/6=0

We calculate fractions


(-1050n^2)/2700n^2+3300n^2/2700n^2+7020n/2700n^2+(-2970n)/2700n^2=0

We multiply all the terms by the denominator


(-1050n^2)+3300n^2+7020n+(-2970n)=0

We add all the numbers together, and all the variables

3300n^2+(-1050n^2)+7020n+(-2970n)=0

We get rid of parentheses

3300n^2-1050n^2+7020n-2970n=0

We add all the numbers together, and all the variables

2250n^2+4050n=0

a = 2250; b = 4050; c = 0;
Δ = b2-4ac
Δ = 40502-4·2250·0
Δ = 16402500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16402500}=4050$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4050)-4050}{2*2250}=\frac{-8100}{4500}
=-1+4/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4050)+4050}{2*2250}=\frac{0}{4500}
=0
$