(X-11)(x-11)=3

Solution for (X-11)(x-11)=3 equation:

(X-11)(X-11)=3

We move all terms to the left:

(X-11)(X-11)-(3)=0

We multiply parentheses ..

(+X^2-11X-11X+121)-3=0

We get rid of parentheses

X^2-11X-11X+121-3=0

We add all the numbers together, and all the variables

X^2-22X+118=0

a = 1; b = -22; c = +118;
Δ = b2-4ac
Δ = -222-4·1·118
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{3}}{2*1}=\frac{22-2\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{3}}{2*1}=\frac{22+2\sqrt{3}}{2}
$