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

Solution for -2x(x+3)=2x-1 equation:

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2-8x+1=0

a = -2; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·(-2)·1
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{2}}{2*-2}=\frac{8-6\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{2}}{2*-2}=\frac{8+6\sqrt{2}}{-4}
$