7n(6n+3)=0

Solution for 7n(6n+3)=0 equation:

7n(6n+3)=0

We multiply parentheses

42n^2+21n=0

a = 42; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·42·0
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*42}=\frac{-42}{84}
=-1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*42}=\frac{0}{84}
=0
$