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

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

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

18x^2-9x+1=0

a = 18; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·18·1
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{-(-9)-3}{2*18}=\frac{6}{36}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3}{2*18}=\frac{12}{36}
=1/3
$