N(y)=7y-1/y+2

Solution for N(y)=7y-1/y+2 equation:

(N)=7N-1/N+2

We move all terms to the left:

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


Domain of the equation: N+2)!=0

N∈R


We get rid of parentheses

N-7N+1/N-2=0

We multiply all the terms by the denominator


N*N-7N*N-2*N+1=0

We add all the numbers together, and all the variables

-2N+N*N-7N*N+1=0

Wy multiply elements

N^2-7N^2-2N+1=0

We add all the numbers together, and all the variables

-6N^2-2N+1=0

a = -6; b = -2; c = +1;
Δ = b2-4ac
Δ = -22-4·(-6)·1
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{7}}{2*-6}=\frac{2-2\sqrt{7}}{-12}
$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{7}}{2*-6}=\frac{2+2\sqrt{7}}{-12}
$