6x(x-2)=24

Solution for 6x(x-2)=24 equation:

6x(x-2)=24

We move all terms to the left:

6x(x-2)-(24)=0

We multiply parentheses

6x^2-12x-24=0

a = 6; b = -12; c = -24;
Δ = b2-4ac
Δ = -122-4·6·(-24)
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{-(-12)-12\sqrt{5}}{2*6}=\frac{12-12\sqrt{5}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{5}}{2*6}=\frac{12+12\sqrt{5}}{12}
$