(x+2)(x+13)=12

Solution for (x+2)(x+13)=12 equation:

(x+2)(x+13)=12

We move all terms to the left:

(x+2)(x+13)-(12)=0

We multiply parentheses ..

(+x^2+13x+2x+26)-12=0

We get rid of parentheses

x^2+13x+2x+26-12=0

We add all the numbers together, and all the variables

x^2+15x+14=0

a = 1; b = 15; c = +14;
Δ = b2-4ac
Δ = 152-4·1·14
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-13}{2*1}=\frac{-28}{2}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+13}{2*1}=\frac{-2}{2}
=-1
$