1.25x=x^2-0.25

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

1.25x=x^2-0.25

We move all terms to the left:

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

We get rid of parentheses

-x^2+1.25x+0.25=0

We add all the numbers together, and all the variables

-1x^2+1.25x+0.25=0

a = -1; b = 1.25; c = +0.25;
Δ = b2-4ac
Δ = 1.252-4·(-1)·0.25
Δ = 2.5625
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{-(1.25)-\sqrt{2.5625}}{2*-1}=\frac{-1.25-\sqrt{2.5625}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.25)+\sqrt{2.5625}}{2*-1}=\frac{-1.25+\sqrt{2.5625}}{-2}
$