0.5x^2+3x=-2

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

0.5x^2+3x=-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

0.5x^2+3x+2=0

a = 0.5; b = 3; c = +2;
Δ = b2-4ac
Δ = 32-4·0.5·2
Δ = 5
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{5}}{2*0.5}=\frac{-3-\sqrt{5}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{5}}{2*0.5}=\frac{-3+\sqrt{5}}{1}
$