.5-x-1.5x^2=0

Solution for .5-x-1.5x^2=0 equation:

.5-x-1.5x^2=0

We add all the numbers together, and all the variables

-1.5x^2-1x+0.5=0

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

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-2}{2*-1.5}=\frac{-1}{-3}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+2}{2*-1.5}=\frac{3}{-3}
=-1
$