x=6x^2-4

Solution for x=6x^2-4 equation:

x=6x^2-4

We move all terms to the left:

x-(6x^2-4)=0

We get rid of parentheses

-6x^2+x+4=0

a = -6; b = 1; c = +4;
Δ = b2-4ac
Δ = 12-4·(-6)·4
Δ = 97
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{97}}{2*-6}=\frac{-1-\sqrt{97}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{97}}{2*-6}=\frac{-1+\sqrt{97}}{-12}
$