(3n-8)(2n+6)=0

Solution for (3n-8)(2n+6)=0 equation:

(3n-8)(2n+6)=0

We multiply parentheses ..

(+6n^2+18n-16n-48)=0

We get rid of parentheses

6n^2+18n-16n-48=0

We add all the numbers together, and all the variables

6n^2+2n-48=0

a = 6; b = 2; c = -48;
Δ = b2-4ac
Δ = 22-4·6·(-48)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-34}{2*6}=\frac{-36}{12}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+34}{2*6}=\frac{32}{12}
=2+2/3
$