(x+8)(x+11)=11

Solution for (x+8)(x+11)=11 equation:

(x+8)(x+11)=11

We move all terms to the left:

(x+8)(x+11)-(11)=0

We multiply parentheses ..

(+x^2+11x+8x+88)-11=0

We get rid of parentheses

x^2+11x+8x+88-11=0

We add all the numbers together, and all the variables

x^2+19x+77=0

a = 1; b = 19; c = +77;
Δ = b2-4ac
Δ = 192-4·1·77
Δ = 53
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{53}}{2*1}=\frac{-19-\sqrt{53}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{53}}{2*1}=\frac{-19+\sqrt{53}}{2}
$