.5x^2+x-1.5=6

Solution for .5x^2+x-1.5=6 equation:

.5x^2+x-1.5=6

We move all terms to the left:

.5x^2+x-1.5-(6)=0

We add all the numbers together, and all the variables

.5x^2+x-7.5=0

a = .5; b = 1; c = -7.5;
Δ = b2-4ac
Δ = 12-4·.5·(-7.5)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-4}{2*.5}=\frac{-5}{1}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+4}{2*.5}=\frac{3}{1}
=3
$