x^2-2x=11.25=0

Solution for x^2-2x=11.25=0 equation:

x^2-2x=11.25=0

We move all terms to the left:

x^2-2x-(11.25)=0

We add all the numbers together, and all the variables

x^2-2x-11.25=0

a = 1; b = -2; c = -11.25;
Δ = b2-4ac
Δ = -22-4·1·(-11.25)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-7}{2*1}=\frac{-5}{2}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+7}{2*1}=\frac{9}{2}
=4+1/2
$