x=3x^2-3

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

x=3x^2-3

We move all terms to the left:

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

We get rid of parentheses

-3x^2+x+3=0

a = -3; b = 1; c = +3;
Δ = b2-4ac
Δ = 12-4·(-3)·3
Δ = 37
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{37}}{2*-3}=\frac{-1-\sqrt{37}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{37}}{2*-3}=\frac{-1+\sqrt{37}}{-6}
$