x(x+1)=3-x

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

x(x+1)=3-x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+2x-3=0

a = 1; b = 2; c = -3;
Δ = b2-4ac
Δ = 22-4·1·(-3)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4}{2*1}=\frac{2}{2}
=1
$