x^2-3x=0.5

Solution for x^2-3x=0.5 equation:

x^2-3x=0.5

We move all terms to the left:

x^2-3x-(0.5)=0

We add all the numbers together, and all the variables

x^2-3x-0.5=0

a = 1; b = -3; c = -0.5;
Δ = b2-4ac
Δ = -32-4·1·(-0.5)
Δ = 11
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{-(-3)-\sqrt{11}}{2*1}=\frac{3-\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{11}}{2*1}=\frac{3+\sqrt{11}}{2}
$