(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^2-4n-7=0

a = 3; b = -4; c = -7;
Δ = b2-4ac
Δ = -42-4·3·(-7)
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{-(-4)-10}{2*3}=\frac{-6}{6}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10}{2*3}=\frac{14}{6}
=2+1/3
$