2-x=0.25x^2-1

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

2-x=0.25x^2-1

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-0.25x^2-1x+3=0

a = -0.25; b = -1; c = +3;
Δ = b2-4ac
Δ = -12-4·(-0.25)·3
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-2}{2*-0.25}=\frac{-1}{-0.5}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+2}{2*-0.25}=\frac{3}{-0.5}
=-6
$