3x^2-1=-x

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

3x^2-1=-x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

3x^2+1x-1=0

We add all the numbers together, and all the variables

3x^2+x-1=0

a = 3; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·3·(-1)
Δ = 13
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{-(1)-\sqrt{13}}{2*3}=\frac{-1-\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{13}}{2*3}=\frac{-1+\sqrt{13}}{6}
$