-3x(x-8)=24

Solution for -3x(x-8)=24 equation:

-3x(x-8)=24

We move all terms to the left:

-3x(x-8)-(24)=0

We multiply 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}
$