N=7/3n-22-4n

Solution for N=7/3n-22-4n equation:

=7/3N-22-4N

We move all terms to the left:

-(7/3N-22-4N)=0


Domain of the equation: 3N-22-4N)!=0

We move all terms containing N to the left, all other terms to the right

3N-4N)!=22

N∈R


We add all the numbers together, and all the variables

-(-4N+7/3N-22)=0

We get rid of parentheses

4N-7/3N+22=0

We multiply all the terms by the denominator


4N*3N+22*3N-7=0

Wy multiply elements

12N^2+66N-7=0

a = 12; b = 66; c = -7;
Δ = b2-4ac
Δ = 662-4·12·(-7)
Δ = 4692
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:

$\sqrt{\Delta}=\sqrt{4692}=\sqrt{4*1173}=\sqrt{4}*\sqrt{1173}=2\sqrt{1173}$
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1173}}{2*12}=\frac{-66-2\sqrt{1173}}{24}
$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1173}}{2*12}=\frac{-66+2\sqrt{1173}}{24}
$