2/9n-4/15=1/6n+1

Solution for 2/9n-4/15=1/6n+1 equation:

2/9n-4/15=1/6n+1

We move all terms to the left:

2/9n-4/15-(1/6n+1)=0


Domain of the equation: 9n!=0

n!=0/9

n!=0

n∈R



Domain of the equation: 6n+1)!=0

n∈R


We get rid of parentheses

2/9n-1/6n-1-4/15=0

We calculate fractions


(-1296n^2)/810n^2+180n/810n^2+(-135n)/810n^2-1=0

We multiply all the terms by the denominator


(-1296n^2)+180n+(-135n)-1*810n^2=0

Wy multiply elements

(-1296n^2)-810n^2+180n+(-135n)=0

We get rid of parentheses

-1296n^2-810n^2+180n-135n=0

We add all the numbers together, and all the variables

-2106n^2+45n=0

a = -2106; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·(-2106)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*-2106}=\frac{-90}{-4212}
=5/234
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*-2106}=\frac{0}{-4212}
=0
$