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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(3(x-2)x), so:

3(x-2)x

We multiply parentheses

3x^2-6x

Back to the equation:

-(3x^2-6x)


We get rid of parentheses

-3x^2+3x+6x-6=0

We add all the numbers together, and all the variables

-3x^2+9x-6=0

a = -3; b = 9; c = -6;
Δ = b2-4ac
Δ = 92-4·(-3)·(-6)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3}{2*-3}=\frac{-12}{-6}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3}{2*-3}=\frac{-6}{-6}
=1
$