3(x-8)x=12

Solution for 3(x-8)x=12 equation:

3(x-8)x=12

We move all terms to the left:

3(x-8)x-(12)=0

We multiply parentheses

3x^2-24x-12=0

a = 3; b = -24; c = -12;
Δ = b2-4ac
Δ = -242-4·3·(-12)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{5}}{2*3}=\frac{24-12\sqrt{5}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{5}}{2*3}=\frac{24+12\sqrt{5}}{6}
$