120=6x^2+4x

Solution for 120=6x^2+4x equation:

120=6x^2+4x

We move all terms to the left:

120-(6x^2+4x)=0

We get rid of parentheses

-6x^2-4x+120=0

a = -6; b = -4; c = +120;
Δ = b2-4ac
Δ = -42-4·(-6)·120
Δ = 2896
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:

$\sqrt{\Delta}=\sqrt{2896}=\sqrt{16*181}=\sqrt{16}*\sqrt{181}=4\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{181}}{2*-6}=\frac{4-4\sqrt{181}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{181}}{2*-6}=\frac{4+4\sqrt{181}}{-12}
$