(x-10)(x-10)=384

Solution for (x-10)(x-10)=384 equation:

(x-10)(x-10)=384

We move all terms to the left:

(x-10)(x-10)-(384)=0

We multiply parentheses ..

(+x^2-10x-10x+100)-384=0

We get rid of parentheses

x^2-10x-10x+100-384=0

We add all the numbers together, and all the variables

x^2-20x-284=0

a = 1; b = -20; c = -284;
Δ = b2-4ac
Δ = -202-4·1·(-284)
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-16\sqrt{6}}{2*1}=\frac{20-16\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+16\sqrt{6}}{2*1}=\frac{20+16\sqrt{6}}{2}
$