2x(5x-6)=120

Solution for 2x(5x-6)=120 equation:

2x(5x-6)=120

We move all terms to the left:

2x(5x-6)-(120)=0

We multiply parentheses

10x^2-12x-120=0

a = 10; b = -12; c = -120;
Δ = b2-4ac
Δ = -122-4·10·(-120)
Δ = 4944
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:

$\sqrt{\Delta}=\sqrt{4944}=\sqrt{16*309}=\sqrt{16}*\sqrt{309}=4\sqrt{309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{309}}{2*10}=\frac{12-4\sqrt{309}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{309}}{2*10}=\frac{12+4\sqrt{309}}{20}
$