(x+5)(x+12)=18

Solution for (x+5)(x+12)=18 equation:

(x+5)(x+12)=18

We move all terms to the left:

(x+5)(x+12)-(18)=0

We multiply parentheses ..

(+x^2+12x+5x+60)-18=0

We get rid of parentheses

x^2+12x+5x+60-18=0

We add all the numbers together, and all the variables

x^2+17x+42=0

a = 1; b = 17; c = +42;
Δ = b2-4ac
Δ = 172-4·1·42
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-11}{2*1}=\frac{-28}{2}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+11}{2*1}=\frac{-6}{2}
=-3
$