-2x(x+2)=2x+1

Solution for -2x(x+2)=2x+1 equation:

-2x(x+2)=2x+1

We move all terms to the left:

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

We multiply parentheses

-2x^2-4x-(2x+1)=0

We get rid of parentheses

-2x^2-4x-2x-1=0

We add all the numbers together, and all the variables

-2x^2-6x-1=0

a = -2; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·(-2)·(-1)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{7}}{2*-2}=\frac{6-2\sqrt{7}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{7}}{2*-2}=\frac{6+2\sqrt{7}}{-4}
$