2x2-1/6=x-x2

Solution for 2x2-1/6=x-x2 equation:

2x^2-1/6=x-x2

We move all terms to the left:

2x^2-1/6-(x-x2)=0

We add all the numbers together, and all the variables

2x^2-(+x-1x^2)-1/6=0

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2+6x^2-6x-1=0

We add all the numbers together, and all the variables

18x^2-6x-1=0

a = 18; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·18·(-1)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{3}}{2*18}=\frac{6-6\sqrt{3}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{3}}{2*18}=\frac{6+6\sqrt{3}}{36}
$