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

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

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

We move all terms to the left:

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


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

x(3x+9)

We multiply parentheses

3x^2+9x

Back to the equation:

-(3x^2+9x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -3; b = -3; c = +18;
Δ = b2-4ac
Δ = -32-4·(-3)·18
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-15}{2*-3}=\frac{-12}{-6}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+15}{2*-3}=\frac{18}{-6}
=-3
$