8n(6n+9)=0

Solution for 8n(6n+9)=0 equation:

8n(6n+9)=0

We multiply parentheses

48n^2+72n=0

a = 48; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·48·0
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*48}=\frac{-144}{96}
=-1+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*48}=\frac{0}{96}
=0
$