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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-6x-10=0

a = 3; b = -6; c = -10;
Δ = b2-4ac
Δ = -62-4·3·(-10)
Δ = 156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{39}}{2*3}=\frac{6-2\sqrt{39}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{39}}{2*3}=\frac{6+2\sqrt{39}}{6}
$