8(6n+7)(n+6)=0

Solution for 8(6n+7)(n+6)=0 equation:

8(6n+7)(n+6)=0

We multiply parentheses ..

8(+6n^2+36n+7n+42)=0

We multiply parentheses

48n^2+288n+56n+336=0

We add all the numbers together, and all the variables

48n^2+344n+336=0

a = 48; b = 344; c = +336;
Δ = b2-4ac
Δ = 3442-4·48·336
Δ = 53824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{53824}=232$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(344)-232}{2*48}=\frac{-576}{96}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(344)+232}{2*48}=\frac{-112}{96}
=-1+1/6
$