(x+12)(x+2)=144

Solution for (x+12)(x+2)=144 equation:

(x+12)(x+2)=144

We move all terms to the left:

(x+12)(x+2)-(144)=0

We multiply parentheses ..

(+x^2+2x+12x+24)-144=0

We get rid of parentheses

x^2+2x+12x+24-144=0

We add all the numbers together, and all the variables

x^2+14x-120=0

a = 1; b = 14; c = -120;
Δ = b2-4ac
Δ = 142-4·1·(-120)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-26}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+26}{2*1}=\frac{12}{2}
=6
$