(x+40)(x+66)=180

Solution for (x+40)(x+66)=180 equation:

(x+40)(x+66)=180

We move all terms to the left:

(x+40)(x+66)-(180)=0

We multiply parentheses ..

(+x^2+66x+40x+2640)-180=0

We get rid of parentheses

x^2+66x+40x+2640-180=0

We add all the numbers together, and all the variables

x^2+106x+2460=0

a = 1; b = 106; c = +2460;
Δ = b2-4ac
Δ = 1062-4·1·2460
Δ = 1396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1396}=\sqrt{4*349}=\sqrt{4}*\sqrt{349}=2\sqrt{349}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(106)-2\sqrt{349}}{2*1}=\frac{-106-2\sqrt{349}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(106)+2\sqrt{349}}{2*1}=\frac{-106+2\sqrt{349}}{2}
$