(6n+2)(5n-8)=0

Solution for (6n+2)(5n-8)=0 equation:

(6n+2)(5n-8)=0

We multiply parentheses ..

(+30n^2-48n+10n-16)=0

We get rid of parentheses

30n^2-48n+10n-16=0

We add all the numbers together, and all the variables

30n^2-38n-16=0

a = 30; b = -38; c = -16;
Δ = b2-4ac
Δ = -382-4·30·(-16)
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-58}{2*30}=\frac{-20}{60}
=-1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+58}{2*30}=\frac{96}{60}
=1+3/5
$