0=x^2-2x+1/9

Solution for 0=x^2-2x+1/9 equation:

0=x^2-2x+1/9

We move all terms to the left:

0-(x^2-2x+1/9)=0

We add all the numbers together, and all the variables

-(x^2-2x+1/9)=0

We get rid of parentheses

-x^2+2x-1/9=0

We multiply all the terms by the denominator


-x^2*9+2x*9-1=0

Wy multiply elements

-9x^2+18x-1=0

a = -9; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·(-9)·(-1)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-12\sqrt{2}}{2*-9}=\frac{-18-12\sqrt{2}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+12\sqrt{2}}{2*-9}=\frac{-18+12\sqrt{2}}{-18}
$