(n+6)(2n+7)=0

Solution for (n+6)(2n+7)=0 equation:

(n+6)(2n+7)=0

We multiply parentheses ..

(+2n^2+7n+12n+42)=0

We get rid of parentheses

2n^2+7n+12n+42=0

We add all the numbers together, and all the variables

2n^2+19n+42=0

a = 2; b = 19; c = +42;
Δ = b2-4ac
Δ = 192-4·2·42
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-5}{2*2}=\frac{-24}{4}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+5}{2*2}=\frac{-14}{4}
=-3+1/2
$