(7n-5)(n+8)=0

Solution for (7n-5)(n+8)=0 equation:

(7n-5)(n+8)=0

We multiply parentheses ..

(+7n^2+56n-5n-40)=0

We get rid of parentheses

7n^2+56n-5n-40=0

We add all the numbers together, and all the variables

7n^2+51n-40=0

a = 7; b = 51; c = -40;
Δ = b2-4ac
Δ = 512-4·7·(-40)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-61}{2*7}=\frac{-112}{14}
=-8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+61}{2*7}=\frac{10}{14}
=5/7
$