(x+62)(x+40)=180

Solution for (x+62)(x+40)=180 equation:

(x+62)(x+40)=180

We move all terms to the left:

(x+62)(x+40)-(180)=0

We multiply parentheses ..

(+x^2+40x+62x+2480)-180=0

We get rid of parentheses

x^2+40x+62x+2480-180=0

We add all the numbers together, and all the variables

x^2+102x+2300=0

a = 1; b = 102; c = +2300;
Δ = b2-4ac
Δ = 1022-4·1·2300
Δ = 1204
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:

$\sqrt{\Delta}=\sqrt{1204}=\sqrt{4*301}=\sqrt{4}*\sqrt{301}=2\sqrt{301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(102)-2\sqrt{301}}{2*1}=\frac{-102-2\sqrt{301}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102)+2\sqrt{301}}{2*1}=\frac{-102+2\sqrt{301}}{2}
$