-3x(x-6)=x+2-4x

Solution for -3x(x-6)=x+2-4x equation:

-3x(x-6)=x+2-4x

We move all terms to the left:

-3x(x-6)-(x+2-4x)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

-3x^2+18x-(-3x+2)=0

We get rid of parentheses

-3x^2+18x+3x-2=0

We add all the numbers together, and all the variables

-3x^2+21x-2=0

a = -3; b = 21; c = -2;
Δ = b2-4ac
Δ = 212-4·(-3)·(-2)
Δ = 417
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{417}}{2*-3}=\frac{-21-\sqrt{417}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{417}}{2*-3}=\frac{-21+\sqrt{417}}{-6}
$