x^2-2.5x+1=0.002

Solution for x^2-2.5x+1=0.002 equation:

x^2-2.5x+1=0.002

We move all terms to the left:

x^2-2.5x+1-(0.002)=0

We add all the numbers together, and all the variables

x^2-2.5x+0.998=0

a = 1; b = -2.5; c = +0.998;
Δ = b2-4ac
Δ = -2.52-4·1·0.998
Δ = 2.258
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{-(-2.5)-\sqrt{2.258}}{2*1}=\frac{2.5-\sqrt{2.258}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.5)+\sqrt{2.258}}{2*1}=\frac{2.5+\sqrt{2.258}}{2}
$