(x-10)(x-10)=200

Solution for (x-10)(x-10)=200 equation:

(x-10)(x-10)=200

We move all terms to the left:

(x-10)(x-10)-(200)=0

We multiply parentheses ..

(+x^2-10x-10x+100)-200=0

We get rid of parentheses

x^2-10x-10x+100-200=0

We add all the numbers together, and all the variables

x^2-20x-100=0

a = 1; b = -20; c = -100;
Δ = b2-4ac
Δ = -202-4·1·(-100)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{2}}{2*1}=\frac{20-20\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{2}}{2*1}=\frac{20+20\sqrt{2}}{2}
$