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

Solution for (x-5)(x-11)=0 equation:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-16x+55=0

a = 1; b = -16; c = +55;
Δ = b2-4ac
Δ = -162-4·1·55
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-6}{2*1}=\frac{10}{2}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+6}{2*1}=\frac{22}{2}
=11
$