3(x^2-72x-288)=0

Solution for 3(x^2-72x-288)=0 equation:

3(x^2-72x-288)=0

We multiply parentheses

3x^2-216x-864=0

a = 3; b = -216; c = -864;
Δ = b2-4ac
Δ = -2162-4·3·(-864)
Δ = 57024
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:

$\sqrt{\Delta}=\sqrt{57024}=\sqrt{5184*11}=\sqrt{5184}*\sqrt{11}=72\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-72\sqrt{11}}{2*3}=\frac{216-72\sqrt{11}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+72\sqrt{11}}{2*3}=\frac{216+72\sqrt{11}}{6}
$