(x-5)(x-11)=27

Solution for (x-5)(x-11)=27 equation:

(x-5)(x-11)=27

We move all terms to the left:

(x-5)(x-11)-(27)=0

We multiply parentheses ..

(+x^2-11x-5x+55)-27=0

We get rid of parentheses

x^2-11x-5x+55-27=0

We add all the numbers together, and all the variables

x^2-16x+28=0

a = 1; b = -16; c = +28;
Δ = b2-4ac
Δ = -162-4·1·28
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-12}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+12}{2*1}=\frac{28}{2}
=14
$