0.5x^2+1x=1.5

Solution for 0.5x^2+1x=1.5 equation:

0.5x^2+1x=1.5

We move all terms to the left:

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

We add all the numbers together, and all the variables

0.5x^2+x-1.5=0

a = 0.5; b = 1; c = -1.5;
Δ = b2-4ac
Δ = 12-4·0.5·(-1.5)
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*0.5}=\frac{-3}{1}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+2}{2*0.5}=\frac{1}{1}
=1
$