x(x-1)=0.25

Solution for x(x-1)=0.25 equation:

x(x-1)=0.25

We move all terms to the left:

x(x-1)-(0.25)=0

We add all the numbers together, and all the variables

x(x-1)-0.25=0

We multiply parentheses

x^2-1x-0.25=0

a = 1; b = -1; c = -0.25;
Δ = b2-4ac
Δ = -12-4·1·(-0.25)
Δ = 2
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{2}}{2*1}=\frac{1-\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{2}}{2*1}=\frac{1+\sqrt{2}}{2}
$