0,25x2-0,5x-0,25=1

Solution for 0,25x2-0,5x-0,25=1 equation:

0.25x^2-0.5x-0.25=1

We move all terms to the left:

0.25x^2-0.5x-0.25-(1)=0

We add all the numbers together, and all the variables

0.25x^2-0.5x-1.25=0

a = 0.25; b = -0.5; c = -1.25;
Δ = b2-4ac
Δ = -0.52-4·0.25·(-1.25)
Δ = 1.5
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{-(-0.5)-\sqrt{1.5}}{2*0.25}=\frac{0.5-\sqrt{1.5}}{0.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{1.5}}{2*0.25}=\frac{0.5+\sqrt{1.5}}{0.5}
$