0.5x^2-2x-3=-3x+1

Solution for 0.5x^2-2x-3=-3x+1 equation:

0.5x^2-2x-3=-3x+1

We move all terms to the left:

0.5x^2-2x-3-(-3x+1)=0

We get rid of parentheses

0.5x^2-2x+3x-1-3=0

We add all the numbers together, and all the variables

0.5x^2+x-4=0

a = 0.5; b = 1; c = -4;
Δ = b2-4ac
Δ = 12-4·0.5·(-4)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3}{2*0.5}=\frac{-4}{1}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*0.5}=\frac{2}{1}
=2
$