2x-2=-4x^2+16x-12

Solution for 2x-2=-4x^2+16x-12 equation:

2x-2=-4x^2+16x-12

We move all terms to the left:

2x-2-(-4x^2+16x-12)=0

We get rid of parentheses

4x^2-16x+2x+12-2=0

We add all the numbers together, and all the variables

4x^2-14x+10=0

a = 4; b = -14; c = +10;
Δ = b2-4ac
Δ = -142-4·4·10
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6}{2*4}=\frac{20}{8}
=2+1/2
$