-6x=4x^2-4

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

-6x=4x^2-4

We move all terms to the left:

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

We get rid of parentheses

-4x^2-6x+4=0

a = -4; b = -6; c = +4;
Δ = b2-4ac
Δ = -62-4·(-4)·4
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10}{2*-4}=\frac{-4}{-8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*-4}=\frac{16}{-8}
=-2
$