0=-0.5x^2+3x+8

Solution for 0=-0.5x^2+3x+8 equation:

0=-0.5x^2+3x+8

We move all terms to the left:

0-(-0.5x^2+3x+8)=0

We add all the numbers together, and all the variables

-(-0.5x^2+3x+8)=0

We get rid of parentheses

0.5x^2-3x-8=0

a = 0.5; b = -3; c = -8;
Δ = b2-4ac
Δ = -32-4·0.5·(-8)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5}{2*0.5}=\frac{-2}{1}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*0.5}=\frac{8}{1}
=8
$