(x+37)(x+67)=180

Solution for (x+37)(x+67)=180 equation:

(x+37)(x+67)=180

We move all terms to the left:

(x+37)(x+67)-(180)=0

We multiply parentheses ..

(+x^2+67x+37x+2479)-180=0

We get rid of parentheses

x^2+67x+37x+2479-180=0

We add all the numbers together, and all the variables

x^2+104x+2299=0

a = 1; b = 104; c = +2299;
Δ = b2-4ac
Δ = 1042-4·1·2299
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(104)-18\sqrt{5}}{2*1}=\frac{-104-18\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(104)+18\sqrt{5}}{2*1}=\frac{-104+18\sqrt{5}}{2}
$