x^2-x+0.078=0

Solution for x^2-x+0.078=0 equation:

x^2-x+0.078=0

We add all the numbers together, and all the variables

x^2-1x+0.078=0

a = 1; b = -1; c = +0.078;
Δ = b2-4ac
Δ = -12-4·1·0.078
Δ = 0.688
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{-(-1)-\sqrt{0.688}}{2*1}=\frac{1-\sqrt{0.688}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{0.688}}{2*1}=\frac{1+\sqrt{0.688}}{2}
$