x^2=x-0.025

Solution for x^2=x-0.025 equation:

x^2=x-0.025

We move all terms to the left:

x^2-(x-0.025)=0

We get rid of parentheses

x^2-x+0.025=0

We add all the numbers together, and all the variables

x^2-1x+0.025=0

a = 1; b = -1; c = +0.025;
Δ = b2-4ac
Δ = -12-4·1·0.025
Δ = 0.9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{0.9}}{2*1}=\frac{1-\sqrt{0.9}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{0.9}}{2*1}=\frac{1+\sqrt{0.9}}{2}
$