20x^2-1=x

Solution for 20x^2-1=x equation:

20x^2-1=x

We move all terms to the left:

20x^2-1-(x)=0

We add all the numbers together, and all the variables

20x^2-1x-1=0

a = 20; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·20·(-1)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*20}=\frac{-8}{40}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*20}=\frac{10}{40}
=1/4
$