-8n(4n-9)=0

Solution for -8n(4n-9)=0 equation:

-8n(4n-9)=0

We multiply parentheses

-32n^2+72n=0

a = -32; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·(-32)·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72}{2*-32}=\frac{-144}{-64}
=2+1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*-32}=\frac{0}{-64}
=0
$