N(-6n-5)=-6n^2-5n

Solution for N(-6n-5)=-6n^2-5n equation:

(-6N-5)=-6N^2-5N

We move all terms to the left:

(-6N-5)-(-6N^2-5N)=0

We get rid of parentheses

6N^2+5N-6N-5=0

We add all the numbers together, and all the variables

6N^2-1N-5=0

a = 6; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·6·(-5)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*6}=\frac{-10}{12}
=-5/6
$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*6}=\frac{12}{12}
=1
$