6x+18=2x(3x+9)

Solution for 6x+18=2x(3x+9) equation:

6x+18=2x(3x+9)

We move all terms to the left:

6x+18-(2x(3x+9))=0


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

2x(3x+9)

We multiply parentheses

6x^2+18x

Back to the equation:

-(6x^2+18x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-6x^2-12x+18=0

a = -6; b = -12; c = +18;
Δ = b2-4ac
Δ = -122-4·(-6)·18
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-24}{2*-6}=\frac{-12}{-12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24}{2*-6}=\frac{36}{-12}
=-3
$