x=0.25x^2-1.25

Solution for x=0.25x^2-1.25 equation:

x=0.25x^2-1.25

We move all terms to the left:

x-(0.25x^2-1.25)=0

We get rid of parentheses

-0.25x^2+x+1.25=0

a = -0.25; b = 1; c = +1.25;
Δ = b2-4ac
Δ = 12-4·(-0.25)·1.25
Δ = 2.25
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{2.25}}{2*-0.25}=\frac{-1-\sqrt{2.25}}{-0.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{2.25}}{2*-0.25}=\frac{-1+\sqrt{2.25}}{-0.5}
$