3(x^2-6x-120)=0

Solution for 3(x^2-6x-120)=0 equation:

3(x^2-6x-120)=0

We multiply parentheses

3x^2-18x-360=0

a = 3; b = -18; c = -360;
Δ = b2-4ac
Δ = -182-4·3·(-360)
Δ = 4644
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:

$\sqrt{\Delta}=\sqrt{4644}=\sqrt{36*129}=\sqrt{36}*\sqrt{129}=6\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{129}}{2*3}=\frac{18-6\sqrt{129}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{129}}{2*3}=\frac{18+6\sqrt{129}}{6}
$