7n^2=-64n-64

Solution for 7n^2=-64n-64 equation:

7n^2=-64n-64

We move all terms to the left:

7n^2-(-64n-64)=0

We get rid of parentheses

7n^2+64n+64=0

a = 7; b = 64; c = +64;
Δ = b2-4ac
Δ = 642-4·7·64
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-48}{2*7}=\frac{-112}{14}
=-8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+48}{2*7}=\frac{-16}{14}
=-1+1/7
$