x=-x2-2x+3

Solution for x=-x2-2x+3 equation:

x=-x2-2x+3

We move all terms to the left:

x-(-x2-2x+3)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+3x-3=0

a = 1; b = 3; c = -3;
Δ = b2-4ac
Δ = 32-4·1·(-3)
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{21}}{2*1}=\frac{-3-\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{21}}{2*1}=\frac{-3+\sqrt{21}}{2}
$