(3n-4)(6n+6)=0

Solution for (3n-4)(6n+6)=0 equation:

(3n-4)(6n+6)=0

We multiply parentheses ..

(+18n^2+18n-24n-24)=0

We get rid of parentheses

18n^2+18n-24n-24=0

We add all the numbers together, and all the variables

18n^2-6n-24=0

a = 18; b = -6; c = -24;
Δ = b2-4ac
Δ = -62-4·18·(-24)
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{-(-6)-42}{2*18}=\frac{-36}{36}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+42}{2*18}=\frac{48}{36}
=1+1/3
$