-6n(4n-7)=0

Solution for -6n(4n-7)=0 equation:

-6n(4n-7)=0

We multiply parentheses

-24n^2+42n=0

a = -24; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·(-24)·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*-24}=\frac{-84}{-48}
=1+3/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*-24}=\frac{0}{-48}
=0
$