(x+58)(x+138)=180

Solution for (x+58)(x+138)=180 equation:

(x+58)(x+138)=180

We move all terms to the left:

(x+58)(x+138)-(180)=0

We multiply parentheses ..

(+x^2+138x+58x+8004)-180=0

We get rid of parentheses

x^2+138x+58x+8004-180=0

We add all the numbers together, and all the variables

x^2+196x+7824=0

a = 1; b = 196; c = +7824;
Δ = b2-4ac
Δ = 1962-4·1·7824
Δ = 7120
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:

$\sqrt{\Delta}=\sqrt{7120}=\sqrt{16*445}=\sqrt{16}*\sqrt{445}=4\sqrt{445}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(196)-4\sqrt{445}}{2*1}=\frac{-196-4\sqrt{445}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(196)+4\sqrt{445}}{2*1}=\frac{-196+4\sqrt{445}}{2}
$