(3n-1)(n+3)=0

Solution for (3n-1)(n+3)=0 equation:

(3n-1)(n+3)=0

We multiply parentheses ..

(+3n^2+9n-1n-3)=0

We get rid of parentheses

3n^2+9n-1n-3=0

We add all the numbers together, and all the variables

3n^2+8n-3=0

a = 3; b = 8; c = -3;
Δ = b2-4ac
Δ = 82-4·3·(-3)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-10}{2*3}=\frac{-18}{6}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+10}{2*3}=\frac{2}{6}
=1/3
$