3x^2=24x-24=0

Solution for 3x^2=24x-24=0 equation:

3x^2=24x-24=0

We move all terms to the left:

3x^2-(24x-24)=0

We get rid of parentheses

3x^2-24x+24=0

a = 3; b = -24; c = +24;
Δ = b2-4ac
Δ = -242-4·3·24
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{2}}{2*3}=\frac{24-12\sqrt{2}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{2}}{2*3}=\frac{24+12\sqrt{2}}{6}
$