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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

(+x^2-3x+x-3)

We get rid of parentheses

x^2-3x+x-3

We add all the numbers together, and all the variables

x^2-2x-3

Back to the equation:

-(x^2-2x-3)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = 2; c = +2;
Δ = b2-4ac
Δ = 22-4·(-1)·2
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{3}}{2*-1}=\frac{-2-2\sqrt{3}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{3}}{2*-1}=\frac{-2+2\sqrt{3}}{-2}
$