(3n+5)(n+6)=0

Solution for (3n+5)(n+6)=0 equation:

(3n+5)(n+6)=0

We multiply parentheses ..

(+3n^2+18n+5n+30)=0

We get rid of parentheses

3n^2+18n+5n+30=0

We add all the numbers together, and all the variables

3n^2+23n+30=0

a = 3; b = 23; c = +30;
Δ = b2-4ac
Δ = 232-4·3·30
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-13}{2*3}=\frac{-36}{6}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+13}{2*3}=\frac{-10}{6}
=-1+2/3
$