4/6-x+x^2/6-x=2

Solution for 4/6-x+x^2/6-x=2 equation:

4/6-x+x^2/6-x=2

We move all terms to the left:

4/6-x+x^2/6-x-(2)=0

determiningTheFunctionDomain
x^2/6-x-x-2+4/6=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x^2-2x*6-8=0

Wy multiply elements

x^2-12x-8=0

a = 1; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·1·(-8)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{11}}{2*1}=\frac{12-4\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{11}}{2*1}=\frac{12+4\sqrt{11}}{2}
$