2x^2-2x+0.3333333=0

Solution for 2x^2-2x+0.3333333=0 equation:

2x^2-2x+0.3333333=0

a = 2; b = -2; c = +0.3333333;
Δ = b2-4ac
Δ = -22-4·2·0.3333333
Δ = 1.3333336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-\sqrt{1.3333336}}{2*2}=\frac{2-\sqrt{1.3333336}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{1.3333336}}{2*2}=\frac{2+\sqrt{1.3333336}}{4}
$