x(3x-9)=120

Solution for x(3x-9)=120 equation:

x(3x-9)=120

We move all terms to the left:

x(3x-9)-(120)=0

We multiply parentheses

3x^2-9x-120=0

a = 3; b = -9; c = -120;
Δ = b2-4ac
Δ = -92-4·3·(-120)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-39}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+39}{2*3}=\frac{48}{6}
=8
$