0.5x2-0.5x-1=0

Solution for 0.5x2-0.5x-1=0 equation:

0.5x^2-0.5x-1=0

a = 0.5; b = -0.5; c = -1;
Δ = b2-4ac
Δ = -0.52-4·0.5·(-1)
Δ = 2.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.5)-\sqrt{2.25}}{2*0.5}=\frac{0.5-\sqrt{2.25}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{2.25}}{2*0.5}=\frac{0.5+\sqrt{2.25}}{1}
$