6x^2-2x=x

Solution for 6x^2-2x=x equation:

6x^2-2x=x

We move all terms to the left:

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

We add all the numbers together, and all the variables

6x^2-3x=0

a = 6; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·6·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*6}=\frac{6}{12}
=1/2
$