1-x=0.25x^2

Solution for 1-x=0.25x^2 equation:

1-x=0.25x^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-0.25x^2-1x+1=0

a = -0.25; b = -1; c = +1;
Δ = b2-4ac
Δ = -12-4·(-0.25)·1
Δ = 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{-(-1)-\sqrt{2}}{2*-0.25}=\frac{1-\sqrt{2}}{-0.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{2}}{2*-0.25}=\frac{1+\sqrt{2}}{-0.5}
$