x=3x^2-1

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

x=3x^2-1

We move all terms to the left:

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

We get rid of parentheses

-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}
$