-x(x+2)+5=(-x)(-x-2)-3

Solution for -x(x+2)+5=(-x)(-x-2)-3 equation:

-x(x+2)+5=(-x)(-x-2)-3

We move all terms to the left:

-x(x+2)+5-((-x)(-x-2)-3)=0

We add all the numbers together, and all the variables

-x(x+2)-((-1x)(-1x-2)-3)+5=0

We multiply parentheses

-x^2-2x-((-1x)(-1x-2)-3)+5=0

We multiply parentheses ..

-x^2-((+x^2+2x)-3)-2x+5=0


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

(+x^2+2x)-3

We get rid of parentheses

x^2+2x-3

Back to the equation:

-(x^2+2x-3)


We add all the numbers together, and all the variables

-1x^2-2x-(x^2+2x-3)+5=0

We get rid of parentheses

-1x^2-x^2-2x-2x+3+5=0

We add all the numbers together, and all the variables

-2x^2-4x+8=0

a = -2; b = -4; c = +8;
Δ = b2-4ac
Δ = -42-4·(-2)·8
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{5}}{2*-2}=\frac{4-4\sqrt{5}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{5}}{2*-2}=\frac{4+4\sqrt{5}}{-4}
$