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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+2x-3=0

a = 2; b = 2; c = -3;
Δ = b2-4ac
Δ = 22-4·2·(-3)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*2}=\frac{-2-2\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*2}=\frac{-2+2\sqrt{7}}{4}
$