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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

(+2x^2+6x-3x-9)+2x=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+5x-9=0

a = 2; b = 5; c = -9;
Δ = b2-4ac
Δ = 52-4·2·(-9)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{97}}{2*2}=\frac{-5-\sqrt{97}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{97}}{2*2}=\frac{-5+\sqrt{97}}{4}
$