0.5x^2+4x+8=32

Solution for 0.5x^2+4x+8=32 equation:

0.5x^2+4x+8=32

We move all terms to the left:

0.5x^2+4x+8-(32)=0

We add all the numbers together, and all the variables

0.5x^2+4x-24=0

a = 0.5; b = 4; c = -24;
Δ = b2-4ac
Δ = 42-4·0.5·(-24)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*0.5}=\frac{-12}{1}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*0.5}=\frac{4}{1}
=4
$