(x-0.5)(x-0.25)=0

Solution for (x-0.5)(x-0.25)=0 equation:

(x-0.5)(x-0.25)=0

We multiply parentheses ..

(+x^2-0.25x-0.5x+0.125)=0

We get rid of parentheses

x^2-0.25x-0.5x+0.125=0

We add all the numbers together, and all the variables

x^2-0.75x+0.125=0

a = 1; b = -0.75; c = +0.125;
Δ = b2-4ac
Δ = -0.752-4·1·0.125
Δ = 0.0625
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{-(-0.75)-\sqrt{0.0625}}{2*1}=\frac{0.75-\sqrt{0.0625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.75)+\sqrt{0.0625}}{2*1}=\frac{0.75+\sqrt{0.0625}}{2}
$