(n+1)(3n+7)=0

Solution for (n+1)(3n+7)=0 equation:

(n+1)(3n+7)=0

We multiply parentheses ..

(+3n^2+7n+3n+7)=0

We get rid of parentheses

3n^2+7n+3n+7=0

We add all the numbers together, and all the variables

3n^2+10n+7=0

a = 3; b = 10; c = +7;
Δ = b2-4ac
Δ = 102-4·3·7
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4}{2*3}=\frac{-14}{6}
=-2+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4}{2*3}=\frac{-6}{6}
=-1
$