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

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

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

We move all terms to the left:

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

We multiply parentheses

3x-(9(x+2)x)+6=0


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

9(x+2)x

We multiply parentheses

9x^2+18x

Back to the equation:

-(9x^2+18x)


We get rid of parentheses

-9x^2+3x-18x+6=0

We add all the numbers together, and all the variables

-9x^2-15x+6=0

a = -9; b = -15; c = +6;
Δ = b2-4ac
Δ = -152-4·(-9)·6
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-21}{2*-9}=\frac{-6}{-18}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+21}{2*-9}=\frac{36}{-18}
=-2
$