x^2-4x-1=1.25

Solution for x^2-4x-1=1.25 equation:

x^2-4x-1=1.25

We move all terms to the left:

x^2-4x-1-(1.25)=0

We add all the numbers together, and all the variables

x^2-4x-2.25=0

a = 1; b = -4; c = -2.25;
Δ = b2-4ac
Δ = -42-4·1·(-2.25)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-5}{2*1}=\frac{-1}{2}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+5}{2*1}=\frac{9}{2}
=4+1/2
$