120-6x=2x*3x

Solution for 120-6x=2x*3x equation:

120-6x=2x*3x

We move all terms to the left:

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

We add all the numbers together, and all the variables

-6x-(+2x*3x)+120=0

We get rid of parentheses

-6x-2x*3x+120=0

Wy multiply elements

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

a = -6; b = -6; c = +120;
Δ = b2-4ac
Δ = -62-4·(-6)·120
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-54}{2*-6}=\frac{-48}{-12}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+54}{2*-6}=\frac{60}{-12}
=-5
$