(x+6)(x+7)=56

Solution for (x+6)(x+7)=56 equation:

(x+6)(x+7)=56

We move all terms to the left:

(x+6)(x+7)-(56)=0

We multiply parentheses ..

(+x^2+7x+6x+42)-56=0

We get rid of parentheses

x^2+7x+6x+42-56=0

We add all the numbers together, and all the variables

x^2+13x-14=0

a = 1; b = 13; c = -14;
Δ = b2-4ac
Δ = 132-4·1·(-14)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-15}{2*1}=\frac{-28}{2}
=-14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+15}{2*1}=\frac{2}{2}
=1
$