2/3n+7=-7-n

Solution for 2/3n+7=-7-n equation:

2/3n+7=-7-n

We move all terms to the left:

2/3n+7-(-7-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-7)+7=0

We get rid of parentheses

2/3n+1n+7+7=0

We multiply all the terms by the denominator


1n*3n+7*3n+7*3n+2=0

Wy multiply elements

3n^2+21n+21n+2=0

We add all the numbers together, and all the variables

3n^2+42n+2=0

a = 3; b = 42; c = +2;
Δ = b2-4ac
Δ = 422-4·3·2
Δ = 1740
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1740}=\sqrt{4*435}=\sqrt{4}*\sqrt{435}=2\sqrt{435}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{435}}{2*3}=\frac{-42-2\sqrt{435}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{435}}{2*3}=\frac{-42+2\sqrt{435}}{6}
$