1.5(x-8)(x-8)=18

Solution for 1.5(x-8)(x-8)=18 equation:

1.5(x-8)(x-8)=18

We move all terms to the left:

1.5(x-8)(x-8)-(18)=0

We multiply parentheses ..

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

We multiply parentheses

1.5x^2-12x-12x+96-18=0

We add all the numbers together, and all the variables

1.5x^2-24x+78=0

a = 1.5; b = -24; c = +78;
Δ = b2-4ac
Δ = -242-4·1.5·78
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{3}}{2*1.5}=\frac{24-6\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{3}}{2*1.5}=\frac{24+6\sqrt{3}}{3}
$