1=x^2-2x-3

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

1=x^2-2x-3

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = 2; c = +4;
Δ = b2-4ac
Δ = 22-4·(-1)·4
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{5}}{2*-1}=\frac{-2-2\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{5}}{2*-1}=\frac{-2+2\sqrt{5}}{-2}
$