N/7n-2(3n+1)=-5+9

Solution for N/7n-2(3n+1)=-5+9 equation:

/7N-2(3N+1)=-5+9

We move all terms to the left:

/7N-2(3N+1)-(-5+9)=0


Domain of the equation: 7N!=0

N!=0/7

N!=0

N∈R


We add all the numbers together, and all the variables

/7N-2(3N+1)-4=0

We multiply parentheses

/7N-6N-2-4=0

We multiply all the terms by the denominator


-6N*7N-2*7N-4*7N+=0

We add all the numbers together, and all the variables

-6N*7N-2*7N-4*7N=0

Wy multiply elements

-42N^2-14N-28N=0

We add all the numbers together, and all the variables

-42N^2-42N=0

a = -42; b = -42; c = 0;
Δ = b2-4ac
Δ = -422-4·(-42)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42}{2*-42}=\frac{0}{-84}
=0
$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42}{2*-42}=\frac{84}{-84}
=-1
$