0=3x(x+2)-9

Solution for 0=3x(x+2)-9 equation:

0=3x(x+2)-9

We move all terms to the left:

0-(3x(x+2)-9)=0

We add all the numbers together, and all the variables

-(3x(x+2)-9)=0


We calculate terms in parentheses: -(3x(x+2)-9), so:

3x(x+2)-9

We multiply parentheses

3x^2+6x-9

Back to the equation:

-(3x^2+6x-9)


We get rid of parentheses

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

a = -3; b = -6; c = +9;
Δ = b2-4ac
Δ = -62-4·(-3)·9
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12}{2*-3}=\frac{-6}{-6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12}{2*-3}=\frac{18}{-6}
=-3
$