.5x+.5x^2=3

Solution for .5x+.5x^2=3 equation:

.5x+.5x^2=3

We move all terms to the left:

.5x+.5x^2-(3)=0

a = .5; b = .5; c = -3;
Δ = b2-4ac
Δ = .52-4·.5·(-3)
Δ = 6.25
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{-(.5)-\sqrt{6.25}}{2*.5}=\frac{-0.5-\sqrt{6.25}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(.5)+\sqrt{6.25}}{2*.5}=\frac{-0.5+\sqrt{6.25}}{1}
$