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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-12x+10=0

a = 2; b = -12; c = +10;
Δ = b2-4ac
Δ = -122-4·2·10
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8}{2*2}=\frac{20}{4}
=5
$