.5(x-8)(x-8)=18

Solution for .5(x-8)(x-8)=18 equation:

.5(x-8)(x-8)=18

We move all terms to the left:

.5(x-8)(x-8)-(18)=0

We multiply parentheses ..

.5(+x^2-8x-8x+64)-18=0

We multiply parentheses

0.5x^2-4x-4x+32-18=0

We add all the numbers together, and all the variables

0.5x^2-8x+14=0

a = 0.5; b = -8; c = +14;
Δ = b2-4ac
Δ = -82-4·0.5·14
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6}{2*0.5}=\frac{2}{1}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6}{2*0.5}=\frac{14}{1}
=14
$