-2x^2-3x-1=x-3

Solution for -2x^2-3x-1=x-3 equation:

-2x^2-3x-1=x-3

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = -4; c = +2;
Δ = b2-4ac
Δ = -42-4·(-2)·2
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{2}}{2*-2}=\frac{4-4\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{2}}{2*-2}=\frac{4+4\sqrt{2}}{-4}
$