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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+x+2=0

a = -1; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-1)·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3}{2*-1}=\frac{-4}{-2}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*-1}=\frac{2}{-2}
=-1
$