(x+6)(x+7)=20

Solution for (x+6)(x+7)=20 equation:

(x+6)(x+7)=20

We move all terms to the left:

(x+6)(x+7)-(20)=0

We multiply parentheses ..

(+x^2+7x+6x+42)-20=0

We get rid of parentheses

x^2+7x+6x+42-20=0

We add all the numbers together, and all the variables

x^2+13x+22=0

a = 1; b = 13; c = +22;
Δ = b2-4ac
Δ = 132-4·1·22
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-9}{2*1}=\frac{-22}{2}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+9}{2*1}=\frac{-4}{2}
=-2
$