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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-(-2x^2)+6x+4=0

We get rid of parentheses

2x^2+6x+4=0

a = 2; b = 6; c = +4;
Δ = b2-4ac
Δ = 62-4·2·4
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2}{2*2}=\frac{-8}{4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2}{2*2}=\frac{-4}{4}
=-1
$