3x-9=3x(x-3)

Solution for 3x-9=3x(x-3) equation:

3x-9=3x(x-3)

We move all terms to the left:

3x-9-(3x(x-3))=0


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

3x(x-3)

We multiply parentheses

3x^2-9x

Back to the equation:

-(3x^2-9x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+12x-9=0

a = -3; b = 12; c = -9;
Δ = b2-4ac
Δ = 122-4·(-3)·(-9)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6}{2*-3}=\frac{-18}{-6}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6}{2*-3}=\frac{-6}{-6}
=1
$