6x(x-8)=32

Solution for 6x(x-8)=32 equation:

6x(x-8)=32

We move all terms to the left:

6x(x-8)-(32)=0

We multiply parentheses

6x^2-48x-32=0

a = 6; b = -48; c = -32;
Δ = b2-4ac
Δ = -482-4·6·(-32)
Δ = 3072
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:

$\sqrt{\Delta}=\sqrt{3072}=\sqrt{1024*3}=\sqrt{1024}*\sqrt{3}=32\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-32\sqrt{3}}{2*6}=\frac{48-32\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+32\sqrt{3}}{2*6}=\frac{48+32\sqrt{3}}{12}
$