-6n(4n-9)=0

Solution for -6n(4n-9)=0 equation:

-6n(4n-9)=0

We multiply parentheses

-24n^2+54n=0

a = -24; b = 54; c = 0;
Δ = b2-4ac
Δ = 542-4·(-24)·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-54}{2*-24}=\frac{-108}{-48}
=2+1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+54}{2*-24}=\frac{0}{-48}
=0
$