(7n-4)(n+8)=0

Solution for (7n-4)(n+8)=0 equation:

(7n-4)(n+8)=0

We multiply parentheses ..

(+7n^2+56n-4n-32)=0

We get rid of parentheses

7n^2+56n-4n-32=0

We add all the numbers together, and all the variables

7n^2+52n-32=0

a = 7; b = 52; c = -32;
Δ = b2-4ac
Δ = 522-4·7·(-32)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-60}{2*7}=\frac{-112}{14}
=-8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+60}{2*7}=\frac{8}{14}
=4/7
$