(3n-2)(3n+4)=0

Solution for (3n-2)(3n+4)=0 equation:

(3n-2)(3n+4)=0

We multiply parentheses ..

(+9n^2+12n-6n-8)=0

We get rid of parentheses

9n^2+12n-6n-8=0

We add all the numbers together, and all the variables

9n^2+6n-8=0

a = 9; b = 6; c = -8;
Δ = b2-4ac
Δ = 62-4·9·(-8)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18}{2*9}=\frac{-24}{18}
=-1+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*9}=\frac{12}{18}
=2/3
$