(x-8)(x-8)-2x=0

Solution for (x-8)(x-8)-2x=0 equation:

(x-8)(x-8)-2x=0

We add all the numbers together, and all the variables

-2x+(x-8)(x-8)=0

We multiply parentheses ..

(+x^2-8x-8x+64)-2x=0

We get rid of parentheses

x^2-8x-8x-2x+64=0

We add all the numbers together, and all the variables

x^2-18x+64=0

a = 1; b = -18; c = +64;
Δ = b2-4ac
Δ = -182-4·1·64
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{17}}{2*1}=\frac{18-2\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{17}}{2*1}=\frac{18+2\sqrt{17}}{2}
$