x^2-0.75=0.25x

Solution for x^2-0.75=0.25x equation:

x^2-0.75=0.25x

We move all terms to the left:

x^2-0.75-(0.25x)=0

We add all the numbers together, and all the variables

x^2-(+0.25x)-0.75=0

We get rid of parentheses

x^2-0.25x-0.75=0

a = 1; b = -0.25; c = -0.75;
Δ = b2-4ac
Δ = -0.252-4·1·(-0.75)
Δ = 3.0625
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{-(-0.25)-\sqrt{3.0625}}{2*1}=\frac{0.25-\sqrt{3.0625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.25)+\sqrt{3.0625}}{2*1}=\frac{0.25+\sqrt{3.0625}}{2}
$