0,5x^2-x-2=2

Solution for 0,5x^2-x-2=2 equation:

0.5x^2-x-2=2

We move all terms to the left:

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

We add all the numbers together, and all the variables

0.5x^2-1x-4=0

a = 0.5; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·0.5·(-4)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3}{2*0.5}=\frac{-2}{1}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3}{2*0.5}=\frac{4}{1}
=4
$