n(-2n-8)=-714

Solution for n(-2n-8)=-714 equation:

n(-2n-8)=-714

We move all terms to the left:

n(-2n-8)-(-714)=0

We add all the numbers together, and all the variables

n(-2n-8)+714=0

We multiply parentheses

-2n^2-8n+714=0

a = -2; b = -8; c = +714;
Δ = b2-4ac
Δ = -82-4·(-2)·714
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-76}{2*-2}=\frac{-68}{-4}
=+17
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+76}{2*-2}=\frac{84}{-4}
=-21
$