x^2-8x+12=16-4x^2

Solution for x^2-8x+12=16-4x^2 equation:

x^2-8x+12=16-4x^2

We move all terms to the left:

x^2-8x+12-(16-4x^2)=0

We get rid of parentheses

x^2+4x^2-8x-16+12=0

We add all the numbers together, and all the variables

5x^2-8x-4=0

a = 5; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·5·(-4)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*5}=\frac{-4}{10}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*5}=\frac{20}{10}
=2
$