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

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

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

We move all terms to the left:

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


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

-3x(3x+9)

We multiply parentheses

-9x^2-27x

Back to the equation:

-(-9x^2-27x)


We get rid of parentheses

9x^2+27x+6x+18=0

We add all the numbers together, and all the variables

9x^2+33x+18=0

a = 9; b = 33; c = +18;
Δ = b2-4ac
Δ = 332-4·9·18
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{-(33)-21}{2*9}=\frac{-54}{18}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+21}{2*9}=\frac{-12}{18}
=-2/3
$