(a+-10)(a+-10)=200

Solution for (a+-10)(a+-10)=200 equation:

(a+-10)(a+-10)=200

We move all terms to the left:

(a+-10)(a+-10)-(200)=0

We add all the numbers together, and all the variables

(a-10)(a-10)-200=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

a^2-20a-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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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