(x-21)(x-31)=2

Solution for (x-21)(x-31)=2 equation:

(x-21)(x-31)=2

We move all terms to the left:

(x-21)(x-31)-(2)=0

We multiply parentheses ..

(+x^2-31x-21x+651)-2=0

We get rid of parentheses

x^2-31x-21x+651-2=0

We add all the numbers together, and all the variables

x^2-52x+649=0

a = 1; b = -52; c = +649;
Δ = b2-4ac
Δ = -522-4·1·649
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-6\sqrt{3}}{2*1}=\frac{52-6\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+6\sqrt{3}}{2*1}=\frac{52+6\sqrt{3}}{2}
$