(11n+13)(n+13)=0

Solution for (11n+13)(n+13)=0 equation:

(11n+13)(n+13)=0

We multiply parentheses ..

(+11n^2+143n+13n+169)=0

We get rid of parentheses

11n^2+143n+13n+169=0

We add all the numbers together, and all the variables

11n^2+156n+169=0

a = 11; b = 156; c = +169;
Δ = b2-4ac
Δ = 1562-4·11·169
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-130}{2*11}=\frac{-286}{22}
=-13
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+130}{2*11}=\frac{-26}{22}
=-1+2/11
$