-3n(4n+7)=0

Solution for -3n(4n+7)=0 equation:

-3n(4n+7)=0

We multiply parentheses

-12n^2-21n=0

a = -12; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-12)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-12}=\frac{0}{-24}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-12}=\frac{42}{-24}
=-1+3/4
$