55=0.5x^2+3x+2

Solution for 55=0.5x^2+3x+2 equation:

55=0.5x^2+3x+2

We move all terms to the left:

55-(0.5x^2+3x+2)=0

We get rid of parentheses

-0.5x^2-3x-2+55=0

We add all the numbers together, and all the variables

-0.5x^2-3x+53=0

a = -0.5; b = -3; c = +53;
Δ = b2-4ac
Δ = -32-4·(-0.5)·53
Δ = 115
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{115}}{2*-0.5}=\frac{3-\sqrt{115}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{115}}{2*-0.5}=\frac{3+\sqrt{115}}{-1}
$