(8n+3)(n+7)=0

Solution for (8n+3)(n+7)=0 equation:

(8n+3)(n+7)=0

We multiply parentheses ..

(+8n^2+56n+3n+21)=0

We get rid of parentheses

8n^2+56n+3n+21=0

We add all the numbers together, and all the variables

8n^2+59n+21=0

a = 8; b = 59; c = +21;
Δ = b2-4ac
Δ = 592-4·8·21
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-53}{2*8}=\frac{-112}{16}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+53}{2*8}=\frac{-6}{16}
=-3/8
$