x=2x^2-4

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

x=2x^2-4

We move all terms to the left:

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

We get rid of parentheses

-2x^2+x+4=0

a = -2; b = 1; c = +4;
Δ = b2-4ac
Δ = 12-4·(-2)·4
Δ = 33
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{33}}{2*-2}=\frac{-1-\sqrt{33}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{33}}{2*-2}=\frac{-1+\sqrt{33}}{-4}
$