(x+3)(x+11)=240

Solution for (x+3)(x+11)=240 equation:

(x+3)(x+11)=240

We move all terms to the left:

(x+3)(x+11)-(240)=0

We multiply parentheses ..

(+x^2+11x+3x+33)-240=0

We get rid of parentheses

x^2+11x+3x+33-240=0

We add all the numbers together, and all the variables

x^2+14x-207=0

a = 1; b = 14; c = -207;
Δ = b2-4ac
Δ = 142-4·1·(-207)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-32}{2*1}=\frac{-46}{2}
=-23
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+32}{2*1}=\frac{18}{2}
=9
$