0.5x^2-3x-1.5=0

Solution for 0.5x^2-3x-1.5=0 equation:

0.5x^2-3x-1.5=0

a = 0.5; b = -3; c = -1.5;
Δ = b2-4ac
Δ = -32-4·0.5·(-1.5)
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-2\sqrt{3}}{2*0.5}=\frac{3-2\sqrt{3}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+2\sqrt{3}}{2*0.5}=\frac{3+2\sqrt{3}}{1}
$