(x+8)(x+5)=180

Solution for (x+8)(x+5)=180 equation:

(x+8)(x+5)=180

We move all terms to the left:

(x+8)(x+5)-(180)=0

We multiply parentheses ..

(+x^2+5x+8x+40)-180=0

We get rid of parentheses

x^2+5x+8x+40-180=0

We add all the numbers together, and all the variables

x^2+13x-140=0

a = 1; b = 13; c = -140;
Δ = b2-4ac
Δ = 132-4·1·(-140)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-27}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+27}{2*1}=\frac{14}{2}
=7
$