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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

-3(x+3)

We multiply parentheses

-3x-9

Back to the equation:

-(-3x-9)


We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+9x+9=0

a = 2; b = 9; c = +9;
Δ = b2-4ac
Δ = 92-4·2·9
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3}{2*2}=\frac{-6}{4}
=-1+1/2
$