x^2-0.05=2x-1

Solution for x^2-0.05=2x-1 equation:

x^2-0.05=2x-1

We move all terms to the left:

x^2-0.05-(2x-1)=0

We get rid of parentheses

x^2-2x+1-0.05=0

We add all the numbers together, and all the variables

x^2-2x+0.95=0

a = 1; b = -2; c = +0.95;
Δ = b2-4ac
Δ = -22-4·1·0.95
Δ = 0.2
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{-(-2)-\sqrt{0.2}}{2*1}=\frac{2-\sqrt{0.2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{0.2}}{2*1}=\frac{2+\sqrt{0.2}}{2}
$