44=0.5x^2+1.5x

Solution for 44=0.5x^2+1.5x equation:

44=0.5x^2+1.5x

We move all terms to the left:

44-(0.5x^2+1.5x)=0

We get rid of parentheses

-0.5x^2-1.5x+44=0

a = -0.5; b = -1.5; c = +44;
Δ = b2-4ac
Δ = -1.52-4·(-0.5)·44
Δ = 90.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1.5)-\sqrt{90.25}}{2*-0.5}=\frac{1.5-\sqrt{90.25}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{90.25}}{2*-0.5}=\frac{1.5+\sqrt{90.25}}{-1}
$