-7n(8n+6)=0

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

-7n(8n+6)=0

We multiply parentheses

-56n^2-42n=0

a = -56; b = -42; c = 0;
Δ = b2-4ac
Δ = -422-4·(-56)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42}{2*-56}=\frac{0}{-112}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42}{2*-56}=\frac{84}{-112}
=-3/4
$