(x-5)(x+7)=-11

Solution for (x-5)(x+7)=-11 equation:

(x-5)(x+7)=-11

We move all terms to the left:

(x-5)(x+7)-(-11)=0

We add all the numbers together, and all the variables

(x-5)(x+7)+11=0

We multiply parentheses ..

(+x^2+7x-5x-35)+11=0

We get rid of parentheses

x^2+7x-5x-35+11=0

We add all the numbers together, and all the variables

x^2+2x-24=0

a = 1; b = 2; c = -24;
Δ = b2-4ac
Δ = 22-4·1·(-24)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*1}=\frac{8}{2}
=4
$