(n+1)(6n+5)=0

Solution for (n+1)(6n+5)=0 equation:

(n+1)(6n+5)=0

We multiply parentheses ..

(+6n^2+5n+6n+5)=0

We get rid of parentheses

6n^2+5n+6n+5=0

We add all the numbers together, and all the variables

6n^2+11n+5=0

a = 6; b = 11; c = +5;
Δ = b2-4ac
Δ = 112-4·6·5
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-1}{2*6}=\frac{-12}{12}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+1}{2*6}=\frac{-10}{12}
=-5/6
$