81x2=x

Solution for 81x2=x equation:

81x^2=x

We move all terms to the left:

81x^2-(x)=0

We add all the numbers together, and all the variables

81x^2-1x=0

a = 81; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·81·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*81}=\frac{0}{162}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*81}=\frac{2}{162}
=1/81
$