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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

8x^2-8x-6=0

a = 8; b = -8; c = -6;
Δ = b2-4ac
Δ = -82-4·8·(-6)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16}{2*8}=\frac{-8}{16}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16}{2*8}=\frac{24}{16}
=1+1/2
$