x(x-2)+x^2-2x+6=3x^2

Solution for x(x-2)+x^2-2x+6=3x^2 equation:

x(x-2)+x^2-2x+6=3x^2

We move all terms to the left:

x(x-2)+x^2-2x+6-(3x^2)=0

determiningTheFunctionDomain
x^2-3x^2+x(x-2)-2x+6=0

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

-1x^2-4x+6=0

a = -1; b = -4; c = +6;
Δ = b2-4ac
Δ = -42-4·(-1)·6
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{10}}{2*-1}=\frac{4-2\sqrt{10}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{10}}{2*-1}=\frac{4+2\sqrt{10}}{-2}
$