2x(3x-8)=120

Solution for 2x(3x-8)=120 equation:

2x(3x-8)=120

We move all terms to the left:

2x(3x-8)-(120)=0

We multiply parentheses

6x^2-16x-120=0

a = 6; b = -16; c = -120;
Δ = b2-4ac
Δ = -162-4·6·(-120)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-56}{2*6}=\frac{-40}{12}
=-3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+56}{2*6}=\frac{72}{12}
=6
$