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

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

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

We move all terms to the left:

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


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

-2x(x+3)

We multiply parentheses

-2x^2-6x

Back to the equation:

-(-2x^2-6x)


We get rid of parentheses

2x^2+6x+x=0

We add all the numbers together, and all the variables

2x^2+7x=0

a = 2; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·2·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*2}=\frac{-14}{4}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*2}=\frac{0}{4}
=0
$